I think LTE is really meant to be usable for voice calls, which would allow a fully packet-switched cell network but
- don't rely on this piece of information without explicit carrier support and software support
- your coverage would be extremely limited anyway
By some distant date like year 2035 it would be possible that the 2G networks are switched off and the freed spectrum used by LTE or LTE-Advanced or revisions of it, and then the lowest common denominator would be LTE instead of GSM.