FWIW, I was a Hammond grinder for years and I know what Hammond soundalikes please me. I don't have a PA series board, but I still have my Korg i30 and the organ sounds in that sound pretty decent to these ears.

To bring in the leslie effect just requires a little extra pressure held on a key. It's not a true leslie speed-up/slow-down (only a real leslie can do that) but for general purposes, it's fine. And there's plenty of tweaks re. percussion, attack, velocity, etc. to play around with. I would think the PA boards are something similar.