I actually think that if Sony acquired any of the 3rd party companies that have Smash reps, getting them in future games would be harder for sure but not impossible.
Not impossible in the sense that Sony would be willing to let their new characters return to a future Smash installment.
I'm 100% sure the company recognizes and knows how big of a franchise Smash is, and if they and their copyright issues cause halts and disturbances on having characters (e.g, Snake, Cloud) return, they know that not only would a fair amount of Nintendo/Smash fans be disappointed or upset, but so would PlayStation fans who also play/own Smash.
As for their general cooperation with Nintendo, I hope they relationship isn't a mere bitter rivalry. I don't think it really is, though I'm curious if Sony's played a role in a few things.
Like for instance, they own the music rights to Xenoblade X. Did they refuse to allow that game's music into Ultimate, or did Nintendo just not want to confront them?
Or, for EVO 2022: Smash isn't in the lineup. I'm confident Nintendo's partnership with Panda played a role in their backing out, but did Sony directly or indirectly play a role in it, too?
Who knows. Just hoping things in general work out nicely for both companies and for Smash.