It depends on a couple of things. If it's 3/4" hardwood (or any SOLID hardwood flooring), there's a good chance it will. Also, if the underlayment is of exterior grade wood, that would help. From there, don't try to 'heat' the floor to dry it out. It's OK to 'fan' the area to keep air moving. You do need to wait a while, perhaps a couple of weeks or so, to see what happens.
The only thing I can say for sure is that assuming the flooring goes down, there's a good chance for some damage. But if it's under the refrigerator, it's out of sight. Hopefully, it's not that unsightly that you will be able to tell when you look at how the fridge is leveled. Wait to see what happends after a few weeks or so, and if the results are not to your likeing, post up again.
My best to ya and hope this helps.
PS: You say it's buckling now, and continuing to do so? Let it.