Yes, it makes perfect sense, but it's too bad that GSX Pro can't be installed where I have Stream, but installs itself in my MSFS 2020
Of course it can and, in fact, it's one of the few installers that support having both the STEAM version and the MS Store version installed at the same time, and it does it in the most proper way: instead of "installing twice", wasting twice the space, it will only install ONE copy, in Addon Manager\MSFS , and if you have both simulator versions installed, it will just create Symbolic links to their respective Community folders, not wasting any more space then it would have, had it installed "real" copies.
However, it won't do that automatically so, assuming you have both versions of the sim installed, first install it into one, then use the drop-down list to select the other, and press Relink there.
The other benefit of using this method with Simbolic links, is that you don't have to worry about updating twice: since both simulators are linked to the same one copy installed, if you update GSX ( or any other FSDT product ), both simulators will see the updated version at the same time.