You gotta try and see.
Depends on tank size, how many parrots, and how mean your FH.
If tank is large enough and your FH is not too mean, he might just chase the parrots for a while and not care about them afterwards and only chase them off if theyre in his way or feeding time.
How many parrots and how large of a tank?
My FH largest FH @ 9" doen't hurt his tank mates And he's scared of grow outs. lol. But same size fishes will get the beat down.