For State ID, it appears the biggest limiting factor would be proof of identity. I can piece together mail or something for residency (bank account statement and maybe mail from their home country embassy). But, if you look here below, the proof of ID options are limited. When we tried, the foreign passport required another document, none of which they had. And the green card couldn't be use for both legal presence and proof of ID.
I think what I'll do is at least generate some mail in their name, or use old mail from consulate and whatever random thing showed up, and add a document stating they've resided in my care and I've unfortunately handled all billing independently. If that doesn't satisfy the interviewing officer and they do need a state ID before being naturalized, we'll re-evaluate the effort.