Yes, I believe inactives gain skills if they use skill objects (like the chess board or workout equipment, for example) like your active sims. It may take until they earn the first skill point to show on their panel, though.
Without a mod or a player to push them, though, few will get far, except maybe with hidden skills like video gaming, hacking, athletic, or something that is on a community lot where they hang out and/or raises fun.