With the release of the latest episode, the answer now appears to be yes.

In Season 7, Episode 7, with the help of an undead dragon, the wall has been melted.

The discussion on if the dragon was breathing fire is discussed below.

Was it Ice or Fire?

One plausible counter argument you could make, is that fire didn't destroy the wall, but rather the magic of the Dragon Fire and/or Night King himself. The wall was created by magic (the details are uncertain), and you could argue it takes magic to destroy magic.