The GFI will function, but you have a code violation here.All of this is 6 gauge wire except the ground to the spa from the spa panel.... It is hooked to the neutral bus on the spa panel. My question is this:
Why did you run that subfeed cable to the little spa panel, then land the neutral and ground on the same bar? Won't effect the operation of the GFCI, but it's still wrong as can be.