Wired GFCI vs. 40v 5a battery use near spa
My guess here is that if the wired TV were to go into the water, a GFCI would be better than nothing, but unsafe...whereas the battery would be practically speaking likely to be completely safe.


120v from an inverter is still 120v.  If that goes into the pool, you could be injured or killed.  Nothing about that is safe.  

The whole idea of a GFCI is that if you drop something into a body of water, the voltage is interrupted once a few mA starts to flow, generally fast enough that you won't be injured.