A lot depends on what your current debt looks like, how many cards you have reporting, how close to maxed out they are, etc.
I can see only two negatives, one short term and one longer term. The short term ding could happen if, during the process of transfer (which can take several weeks) the same balance reports on both the Discover and the original card or cards. That would clear up after the next reporting cycle. The potential longer term problem is if you maxed out your Discover card with the transfer.
Otherwise, shouldn't be a problem.
