Depends on the skills involved.
Anything defensive will simply not work, I beleive (since God Mode pretty much negates all damage, and the skills can't increase because they're not "protecting" you.) I think the offensive and utilitarian skills are not hampered, as God Mode doesn't affect those. THis is from personal expereince, however, so i can't claim its accurate.
Why not go and find out for yuorself? Better yet... think I'll check it out myself. Be right back!
--EDIT--
Ok, done. The Heavy Armor, Medium Armor, Light Armor and Unarmored skills will NOT level up. Block remains unaffected, and most spells will increase when the spell is cast (unlike in Oblivion, where it requires something to be cast ON with some skills.) Weapon skills are unaffected.
So, yeah. You can level up. Just don't expect to increase your chosen armor skill.