Yeah, you can still paint it. I've owned a Trigger so I know what you're talking about, and I've painted a gray rubberized QFR case. The rubbery soft-touch coating is a very thin layer that will come off easily with 400-grit sandpaper. Just go slowly, as it will come off easily from all the edges but will take more work for flat surfaces. Could try 600-grit for those, just remember to smooth out any rough sanding lines afterwards. Just get good quality sandpaper, like by 3M from auto supply shops.
One thing to keep in mind is the logo part that's backlit. It's going to be stepped where you'll see the outline. If that doesn't bother you, just maybe put some electrical tape over it from the back side to prevent LED light bleeding through the paint, as it will likely otherwise do so. And because there are many ridges on the casing, spray in VERY thin layers, just do many of them. If you do thick, you'll end up with too much accumulating in the crevices, and it will not dry evenly there / will look bad. Best to just mist the color on gradually changing directions (rotate the casing periodically) to get all the corners / crevices evenly coated.