We all know 22 LR is dirty because of the lead bullets and will foul a welded suppressor.
Does the same go for 22 Mag?  Can you shoot jacketed 22 Mag bullets through a 5.56 suppressor occasionally without concerns of buildup?
I remember pulling apart 22 Mag rounds and they are full metal jacket with a copper covered base.
Or is the powder and rimfire primer material that is dirty?

The powder on rimfire is really dirty, so you'll get a bunch of that and no lead.  I'd be fine with it as long as your not putting a shitload of rounds through it.

For a quick hunting trip?
Sure, I’d lend a direct thread to a (uncultured) shooting buddy who doesn’t have a rimfire suppressor.
It’s not like a 10/22 or 15/22 where you’re blasting a full bulk pack in a weekend.
It would probably balance like shit.
Ymmv

My .22 mag makes a mess of my rimfire cans. It’s not the lead it’s the powder. In fact my can got so powdered up it caught fire and turned into a snake.

That sounds awesome.  How many of us are going to try to do this on purpose now?

Now I'm wondering if you fowl up a centerfire can with 22 crud will a mag dump of 556 rattle all the crap out of it?

As previously mentioned, the powder from a .22 Magnum does not burn very clean and will leave unburned grains in your barrel and suppressor.   Just fire a few rounds and look down the barrel if you don't believe me.    This unburned powder will also accumulate in the suppressor.    

That said, I would not worry about running .22 Magnum through a sealed centerfire suppressor.   Running some 5.56 through the can will blast/ burn out the unburned residue.    Another method is to use an air compressor to blast out the residue.   I have used both methods with success and have verified they work with a Lane Scorpion 5.56 suppressor which is serviceable can.