Director Meguro has a sample UMD of the upcoming Persona PSP remake and he reports that the loading time seems to shorten for battle encounters if you have a PSP-2000 or newer. Starting off with 5 seconds for the first battle, the loading time gradually decreases to 2 seconds in later encounters. Most likely because of the cache memory added to the newer PSP models.
As for the features that aim to help make levelling a little less laborious, there is the "auto" option to help repeat commands given. Here Meguro gives out commands for the first turn, then turns on auto at the third turn. The battle ended in just over 1 minute. And if you turn on the new option of skipping battle animation too, that time can be cut down to as far as a quarter of its length of 15 seconds. It varies depending on the enemies and party member levels of course and in this case, the MC was at level 14.
Fast enough? I don't know because I never played the original but, I guess I'm going to have to bear with the slower loading times on my first gen PSP.