Trophies

Let's say you play a game that has trophies supported. And when you earn the achievement, does it save the data and info onto the PlayStation account if you are signed in or not? Also, are you able to sign in or up with an active PSN account for RPCS3?

NOTE: I am new to this and haven't come onto the emulator Or site for a long time, please text me back if there's any way or not. Thank you and appreciate those for reading this!