This is an issue that faces only a few but could have potentially disastrous results.
The answer in short is no, do not use your fireplace after any damage has occurred. The reasons to this are past what meets the naked eye. The warranty for gas fireplaces are often void after water damage as most of the issues that can result are often formed inside the unit. The aesthetics may be fine, the flame may still ignite, but what you don't realize is the dangers behind moisture buildup.
Moisture that may have gotten in pipes, fittings, or valves can impede the safe use of the gas fireplace and its features. This can lead to fuel line leakage, improper pressure valve releases, and non-functioning shut off valves. Along with this, common rusting and deteriorating of pipes can eventually lead to fuel leaking thus endangering your family. You do not have to see the issues that may result from water damage, as more often then not, the issues will build over time and can be fatal.
These small and seemingly unnoticeable issues can lead to disastrous results. This is why warranties from most companies are void from such issues. Problems may be difficult to identify and have such a negative result if not correctly fixed.
If something like this has happened to you, please do not use your unit, but talk with a fireplace specialist regarding what has occurred