It will seal it up tight. You would be better off priming the whole wall with it.
Yeah, spot priming with Gardz would certainly make the problem worse.
If you Really don't want to prime the whole wall then I would either use the paint itself as has been mentioned (though I hesitate to do that with a paint like Cashmere that isn't rated to be applied directly to joint compound) or use a low sealing drywall primer. The cheaper the better in this case. That'll prime the patches while still leaving them porous.
Generally when you see language like this in a primers description;
"Valspar Interior Latex Drywall Primer is specifically designed to equalize surface texture differences between sanded tape joints and new drywall, resulting in an extremely uniform finish coat appearance."
That's a primer that isn't designed to seal well, but rather equalizes the surface by creating uniform porosity. It will lower the sheen of an applied finish rather than increasing it which is what caused your shiny spots.
I would either use the paint itself as has been mentioned (though I hesitate to do that with a paint like Cashmere that isn't rated to be applied directly to joint compound)
We've done it many times without issues but I think it might be because we use 18" 3/4 naps and put on more paint. And we use Cashmere most of the time. As long as your big patches and mud spots are done on the first coat it turns out fine. But if you are using a thinner nap then you really have to prime. I've even used a spray oil primer on mud spots and that worked really well.