It is an interesting thought experiment--though it sounds like something from a Ballard or Dick novel--the only thing missing is that the immigrants have some chip integrated into their bodies which the train can read to let them pass (therefore creating a black market in chips and people who will install them illegally for you.)
But on the whole it is a bad idea and I don't think it would do what you say it would do.
I'll bracket the most important and probably most obvious category--that of it's ethical implications--by simply saying that only a science fiction dystopia would go to such extremes at keeping an underclass an underclass or otherwise facilitating their extreme exploitation (with the understanding that in many cases this is how the public transit system operates at the margins.) In other words, I'll just try to look at it as whether it's a good idea that might work, rather than the question of whether it would be right to have such a system.
Pragmatically it would be silly since it doesn't solve the problem of where people live when they get to CA. It doesn't really make sense to have people live in Mexico and trapse up here on even a high speed train daily to work in the fields. The transportation to the fields and from is not the problem: it is the fact that they are illegal, that it is mostly illegal workers who do this work and that the entire industry and surrounding communities seem to live in a parallel universe where the living standards of these workers is undiscussed. During the harvest seasons, as I understand it, the work is pretty much round the clock, with very little time for extensive travel. Giving people a high speed train to leave and come back on two or three times a year isn't all that useful for solving the problem--though I'm sure many people who have to make that trip normally would appreciate a cheap, clean, safe, modern, streamlined process of getting back and forth. It would be far more humane than the current system of death defying feats etc., but in many ways that probably makes it even less likely the rest of the people in the state would agree with it.
Legally, giving even a train card would likely be too official for the industry, which seems to operate on some plausible deniability plane; and once you allow immigrants any official documents, you are basically admitting that they are in the country doing work, which starts to erode the reason you have them doing the work in the first place: namely that you can pay them way below the wages they should be paid in conditions far below acceptable ones. A train is not going to solve the visa or legality problem that already exists. And if you're going to address the latter in order to get the train, you might as well address it without a train--particularly since, as I said above, it doesn't make a lot of practical sense to be able to transport people in and out of the country on a daily basis just to keep them in some legal grey area most of the time.
Finally, the idea that this would be a path to getting a high speed train in the state doesn't account for the severe xenophobia and class/race divides in even the bluest of states (California being purple at best culturally). An anecdote: I used to live in northern virginia. I lived about 4 miles from the pentagon, which is one of the hubs of all the bus traffic going from NOVA to the trains into DC.
In general, the trains are better supported (though they don't cover a lot of ground) I don't know the data on this, but the bus system was generally less reliable in terms of the timing and with fewer buses stopping (sometimes only once every 30 minutes or so) and requiring a lot of complicated transfers to get from most points A -> B. So (maybe just because they can) the white folks tend to drive to the train station and the immigrant and minority population (I'm generalizing here) would take both buses and trains to get around On the other hand, in taking the bus and noticing my fellow riders, I couldn't help but wonder if it's general lack of support and fewer routes came from the perceived marginality of the riders, rather than the other way around).
But I lived in an area where there was not an issue of convenience. There is a major road called Columbia Pike and there are buses nearly every 15 minutes or so (more at rush hour) that will take you to Pentagon and then on the train into the city (where the train system was much more fleshed out). My wife took the bus everyday to work and it was very easy--with the exception that, since it was on the road you had to worry about traffic. But for some reason, there still weren't a lot of white folks riding the bus. The only explanation I can give is that there were a lot of minorities and immigrants in the area and so riding the bus was associated with these populations (mind you there were plenty of anglos too--you could just seem them driving their cars to the city)
I don't know how accurate my assessment is of this perception (i.e. white folks didn't like the bus because the bus was for the minorities and was, consequently often sub-par in terms of performance), but the year before I left, the WMTA started coming to local festivals in the Columbia Pike area pitching the idea of a "streetcar." I stopped by one day to chat with the people doing the presentation and they told me that it would, like the bus, have to share the lane and stop at all signals: in other words there were almost no advantages between this new system--which would require millions in infrastructure and no new train service--and the existing system of very regular bus service on this particular stretch of road. The streetcar project was only for this stretch and it was just supposed to supplement the already regular service for buses, not replace them altogether.
The drawings of this project showed the bourgeois elegance of these transportation machines, but there didn't seem to be anything to give these an advantage over the existing buses except that it might be something the white folks would feel okay about riding. The person giving me the spiel said as much in the most politically correct way possible--that there were a lot of people in the area who simply didn't consider riding buses an option or something like that. In other words, a bunch of white, middle class folks thought they were too good to ride the bus, but would flock to the trains. So if you want them, in Spike Lee's command, to "get on the bus" then you need to make the bus look more like a train. It was a stupid PR approach to the problem that would have cost a lot more than just improving the existing bus system metro wide.
In short, a beta test associating it with the equivalent of slave transports for people below working class is not the best way to get average middle class white* people to use a system of public transportation--much less fund it with their tax dollars.
[I now send this, too late and cloudy headed to really be making statements about sensitive topics. We'll see...]
* I say this with the caveat that in southern california the average middle class people are no longer necessarily white to the same degree as in other parts of the country.