You jest, but it seems appropriate to me to raise an NPC a level or so when time is skipped. Why wouldn't I do the same for the PCs?
If the NPC has been adventuring or similar major achievements off-screen, I might level them up. This would apply only to a minority of highly active NPCs though - and in some campaigns I might also be rolling to see if they get killed.
If your PCs are likewise held to be adventuring off-screen, then sure, give them XP and levels. That might apply to eg the PC who rejoins the group after a long time away. But I would never ever give XP just for 'being alive'.