Yes is the answer. However it is not as easy as some people would try and make you think. Just because you decide to go down this road and actually get yourself a loan does not mean nit is going to be plain sailing from this point onwards, not at all.
You will still have a loan and in some probability that loan will actually be a larger loan than what you owed to your creditors originally. So to sum uo yes you can pay off your debts with a credit card consolidation loan, but the most important thing is to stay disciplined.