I dunno but Sony's gonna Square and I'm gonna keep saying so until I'm right.
They might, they might not. The fact of the matter is, Square wants Sony to acquire them more than Sony wants to acquire Square. At this juncture, Square is effectively a second-party Sony developer that self-publishes. They put out almost nothing on Xbox, little on Nintendo, and their PC ports often run worse than their PS5 counterparts and usually come a good 12 months after the PS5 launch.
Square has been cozying up to Sony in various ways--the whole sale of their western studios and IP to Embracer was very telling. They got very little for those one the surface--but when you look into the details of the deal, the real payout was that Embracer paid off a large chunk of Square's debt. This new, leaner Square has been pushing PS5 exclusives with late PC ports (as Sony itself does), made itself lean and solvent (though shakier with a lot less IP under its belt), and gone so far as publicly praising Sony and the PS5. It's very much a mating dance--"Please acquire us Papa Sony we love you long time!"
If they can be had for relatively low cost, sure, Sony may very well buy them. But in doing so they won't get much out of Square that they aren't already getting. As long as Square keeps giving Sony all the milk, Sony doesn't need to spend the money to buy the cow. However, with yesterday's decision, it's pretty much been declared a free-for-all with no rules in the gaming space. If Square offers themselves up to Sony cheap, then I'd say Sony buys them purely out of fear that if they don't, Microsoft or Nintendo will. In fact, I'd go so far as to say that will be the big impetus between pretty much every developer and publisher buy out going forward--fear that someone else will beat the buyer to the punch.