I was curious so I decided to test out the loading RNG. From my findings it looks like its only the frame you select the save file on that determines the RNG seed.

What I did was create two save files with different names, stages complete, armies, etc. Powered on the game, went to the save load screen, paused emulation. At this point I manually set the global frame counter to a known value, I choose 0x40. Held down the A button and frame advanced to start the loading. Used a joker and got a World card. I then repeated this process for the second save file and was able to pull a World card.

Things that could still be tested: If a game was significantly further into the game and had more data. I don't believe it'd push it into another frame tick but its possible.