The actual MAIN concern is this however....
.22LR is SUPER DIRTY. They leave tons of carbon and lead deposits in the can. The problem with shooting .22 out of a .223 can is that the .223 can is almost always sealed (there's a couple serviceable centerfire cans out there) so you can't get in there to get the junk out. This junk can reduce performance of your suppressor over time, or can get knocked loose when you fire higher-pressure centerfire ammo through it and has the potential to cause baffle strikes.
Do yourself a favor. Get a centerfire can AND a rimfire can. If you don't have the budget for that, skip the centerfire can.
Was look at a DeGroat Tactical Armaments NANO