There's an equivalent to PNG for non-diplomatic staff - "not acceptable". But the same rules apply to both in this regard. If the host country declares someone to have PNG/NA status, and they can do so at any time without explanation, the sending country can either recall them OR terminate their status - "as appropriate". If this isn't done within a reasonable period, the host country is allowed to simply cease to recognise their immunities. At which point they could be arrested.
It's conceivable that Ecuador could appoint Assange to something and then, when Britain inevitably rejects the appointment, cite the "reasonable period" clause to give him enough time to get out of there. But the Convention also allows the host country to reject someone before they even arrive, in which case presumably that clause wouldn't apply, so by analogy I would think that if Britain has already made it clear they wouldn't accept Assange being appointed to anything, Ecuador probably couldn't get away with that. But I don't know if anyone's ever tried it.