Act-Labs USB Gun + VGA666 CRT + Pi 3b+ ?

[Kingcade]

So, as usual I'm in what I believe is uncharted territory. My setup:

Raspberry Pi 3b+ running RetroPie
Monitor is a 31Khz ViewSonic 21" CRT
Pi is connected to the monitor through a VGA666 hat
CRT SwitchRes is enabled, so all of my games run in native resolutions and refresh rates

I'd like to add my Act-Labs PC USB Gun into the mix for Light Gun games. Challenges I see so far:
- no idea if the light gun's VGA box will work with the VGA666 hat
- the changing resolutions and refresh rates will cause me to need to recalibrate every game
- the light gun docs say Windows is required, but I don't know if that's really true

Anyway, I haven't plugged it in yet to see what would happen, but has anyone tried even some element of this setup? Thanks for any advance pointers!