Yes, but the attempt to allocate labour time through the blunt instrument of prices attaching to discrete outputs of those social production relations is already way past its sell-by date. The prices of most basic consumer goods are absurdly low, so that the cost of imposing market discipline is often greater. A friend of mine worked out that the cost of the new ticket barriers on the London underground (early nineties) was greater than the cost of running the service - it would have been cheaper to let people travel for free. A college bursar told me recently that but for the outrage, it would be cheaper for him to give all the students an unlimited Amazon account than keep up the library.
Hybrid economic forms, like the legal titles to immaterial goods (file downloads; CO2 emission rights etc.) are all evidence that the commodity form is a poor approximation to social reproduction today - and that it is falling apart as we speak. Just to pick the most obvious example, the extraordinary size of the state sector is evidence that the basics of social reproduction are simply not doable as private production.
It would be idle to sketch out the precise details, but a non-alienated production process would have its character as process much more explicit, and the unique separation of goods would be correspondingly less important. Of course, that much is already apparent today in the weekly shop, the cable-broadband service contract, schooling, etc.
Fundamental, it seems to me, is that the production system would be - as it is already - well-oiled by superabundance, which ought to reduce the hoarding acquisitive impulse that governs today's buying.