There are a few things to consider with using a Centerfire suppressor with a rimfire weapon.
As others have stated you can't take these cans apart to clean them so lead buildup is a concern. However there are a couple very easy solutions to this. First you can soak them in some pretty harsh solvents that will break up the lead. This is a Nono with .22 cans but centerfire cans are usually steel and iconel. so they hold up fine. The second solution is even easier. Throw it on an AR and blast a mag or two through it. This will heat the can up and burn off the lead particles and blow them right out.
Of bigger concern is the chance of a bafflestrike. .22 ammo is not made to high standards and centerfire cans are much longer This increases the chance of that nasty little bullet bouncing around inside the can. Which is the last thing any of us wants.
Another factor in this is the threading. Sadly just like with the ammo, a lot of companies don't take the care they should with .22 barrel when they thread it. And non concentric threads will cause you to kill your can in short order.
All that being said, it can be done, and I have done it. but you need to know the risks and what to watch out for.