Could they do it? Sure, it's not an impossible scenario, but what would be the reason for it outside of "trolling"? Both Occam's and Hanlon's razor fit easily here.
I think it’s reasonable to assume that a substantial portion of doge employees have roots in /pol/ which itself has roots in /b/. Elon literally carried a sink into Twitter on his first day, I’m sure there’s plenty of similar antics elsewhere.