I think there's a good chance of data corruption if you lose power while saving on PS2. I've had modern saves get corrupted like that, such as recently where I was playing Days Gone and while I saved, the game/system crashed, and then after a recovery, that save had been corrupted. Luckily I had an autosave before that, so I didn't lose like...10 to 15 hours of game time, but it's absolutely a possibility. It's why I think a lot of save prompts say to not turn off the system if the save is happening.
It's why it is usually best to turn off your PC and consoles if the storm is around you. Go read a book, play a portable system, not worth risking things that much.