Nope. In that universe a major big bad bought the warehouse, left the signs up as cover, then moved in his low level minions. It's what you do when you operate your cartel in a major North American city, that for some reason has a dearth of volcanoes in which to build secret bases.
Your theory fails for a very important reason.
We live, according to Grant Morrison, on Earth 33. On Earth 33, KB was bought by Bain Capital.
The MCU takes place on Earth 199999. But Bain Capital would never be a front for a major big bad on Earth 199999.
That's because Earth 199999 exists as a highly profitable fictional universe on Earth 33, where, on Earth 33, Disney/Marvel's use of the name "Bain" as a big bad guy would result in contentious litigation between Disney/Marvel and AT&T/Warner Bros/DC Comics, which owns the trademark and copyrights for supervillains named "Bane" on any and all Earths, real or fictional, regardless of numeric designation of any particular Earth.
Presumably, this would also include homophones of "Bane." Including "Bain."
So, no, there is no way that any major MCU villain would be associated with KB Toys or its erstwhile VC owner, Bain Capital because The One Above The One Above All (to wit, Disney's legal department) would never allow it.
I leave you with some freestyle rap, courtesy of Bane.