There aren't really any spoilers in P4 for P3 except for references to and cameos of minor characters - which are to be expected anyways. You can honestly play them both side by side and it'll be perfectly fine.
Those things are still there. Plus, since the gameplay flows better, P3 might be more difficult to finish when playing side by side, considering how daunting Tartarus is. Plus, she's almost done.
I'd advise against it, but Pumpkin will do what she pleases.