Its YMMV, I've tried in Ohio a few times in different counties (Hamilton & Butler), they just show the list of acceptable documents which does not have "Federal Register" or "I797C" list as one.

The main reason why they do not accept I797C is that the document itself says "This document does not provide immigration benefit......" or something like that.

Some states do provide driving privileges to immigrants regardless of immigration status - OH is not one of those.