Keeping the product alive could be one of the terms of the acquisition, but it seems unlikely - it could lower the offer, and it's unlikely startup founders would throw away money on a matter of principle unless the community promise was somehow legally binding.
In a sense the promise is a "non-credible threat" in game-theoretic terms. It would attract users if they carried it out, but because acquisition happens after the user-attraction stage they don't have an incentive to carry it out. This means they won't rationally carry it out, which means they don't attract rational users. This situation can be avoided if they "tie their own hands".