Is caulk a good temporary fix for a gash in fascia board?
You have to look underneath it. 

The problem with water is that it doesn't just "gash" things, it goes through them and soaks what's behind them, and then it rots it. Take it down, inspect behind everything until you find all of the damage, FIX IT, put it back up. By caulking it, you're just sealing the water in and helping the rot.