Protecting the feeder to the pool equipment subpanel with a GF breaker at the source should not cause any 'false trips' unless there is a fault within the feeder.
That said, in the event there is a GF on any of the branch circuits from the pool subpanel, depending upon the sensitivity of the 50 amp GF breaker, it may trip with or before the branch circuit CB. That's dependent on the sensitivity curves of the breakers, and really 'deep' electrical theory.
Greg may have some input.....
