There is no antialiasing patch for FF7pc. If you use NVIDIA's video card (gf3, gf4ti, fx5600), you can enable 2x2 AA with RivaTuner. It should solve the grid problem in 2D background.
You should not install that XP patch and here's why.Rivatuner can work with the FF7 Chocobo patch, if that's what you're asking. You can get it here.