Does letting Papyrus defeat you count as sparing him for pacifist runs?

in theory, yes. the purpose of Pacifist is that you gain 0 EXP through the entire game, meaning you've harmed 0 and won 0 battles.

Here are the rules of pacifism, with as few spoilers as possible:

1. The game will consider you "a pacifist" as long as you have zero EXP (and LV 1). EXP and LV can both be viewed on the STAT page.
2. The only way to gain EXP (and by extension LV) is to kill a monster. Whether you spared the monster, fled, or did something else entirely, is irrelevant as long as you did not kill them.
3. The only way to kill a monster is by (repeatedly) using the FIGHT option until the monster's HP is depleted. (Some monsters can be killed in one hit.)
4. The flavor texts and enemy dialog that appear between turns often contain hints about how to resolve the battle. They may suggest particular ACTs or other courses of action, depending on the fight.
5. If you make a mistake and earn EXP, you can reload your last SAVE to remove the unwanted EXP. Obviously, you will also erase any progress made since that SAVE.
6. If you earn EXP, the game always tells you so at the end of the battle.