It is hard to tell if this will surely afect you in this case; we would be guessing if we said yes or no to that question.
However, it is not rare that recruiters check your last salary as part of the recruiting process, so they get a better idea of how much to offer you. In a way (recruiter's point of view), so they can give you a better offer than your last job and at the same time so they don't go too far and offer you way much than you earned before. This way they are maximising the cost/benefit of hiring you.
Now, given that you mention they offered that ammount (and not something you requested) it seems to suggest that they are indeed willing and able to pay you that ammount (maybe giving you a good salary so you are tempted to take the job).
It would be unprofessional from their part to take back their word and give you a lower counter-offer; if this happens I suggest you rethink if it is worth working in a company that does not keep their word when they can obtain profit from it.
However, there is also nothing preventing them from "politely" saying you were not selected for the job, when they really just found someone who does the job for less money (here I am speculating, but is one of the possibilities).
For this, I am afraid, there is few things you could do. Only time will tell you for sure if you were selected or not. Hope this words help you out, good luck with your job search.