I would think so. Starbucks was likely evaluating who put the surpringly well put together satire store up, and whether it was just creating good press for them. And then comedy central(or maybe Absolutely productions) heard SB noticed and decided the joke run its course and it was better to avoid a suit. Eventually though, I assume Starbucks would also decide the joke run its course and it's more important to protect IP than let some production company keep running the joke.
“ Starbucks did not pursue legal action, although it did note to the press that it was "evaluating" the possibility while reinforcing that the "Starbucks" name is a protected trademark. Upon the episode's broadcast, it was acclaimed by television critics.”
https://en.m.wikipedia.org/wiki/Dumb_Starbucks