Okay, not sure what you're asking, and going slightly spoiler-y here (so ignore if you don't want spoilers.
First the less spoiler-y thing. Higher rated parts take less damage when training. Diamond skin always takes way less than roboskin, by a lot. So better parts help there.
Next, better parts mean more xp working as well. So when they get a boost to social being a clerk, their parts can still matter.
And for event based damage, you do still take less damage for better parts when a bot is damaged in an event.
Note that psychocore loss is also tied to XP gain, so if you're spending too much time stabilizing your bots and have already maxed out the AI on the capsule? Try less efficient CPU.
You'll get the same payout (cash/AP which is tied to bot skill level) but less bot XP (so they won't level as fast, but won't go crazy as fast either).
Now for the tricky thing. It isn't only the CPU that can boost/lower your training XP gain.
But the parts that matter depends on the skill being trained.
This is in the parts files (so custom mod parts could have differing info) but in general...