You can Fire 17hmr thru your Suppressor.
But, Rimfire cartridges burn very Dirty and will foul up your center fire Suppressor.
Some Suppressor manufacturer don't recommend it.
As far as sound reduction , a 17 hmr goes very fast and the bullet sonic "Crack " will still be there fired thru your suppressor. A Suppressor on most center fire rifles, suppresses the "BOOM" of the powder burn, not the sonic crack of the bullet traveling thru the air.
A rimfire suppressor would be a better choice , but even for it to be quiet you would need to use subsonic ammo. I don't know if there is a sub-sonic 17 hmr ammo.
But I see no harm in trying a round or two to satisfy your curiosity.
Good Luck.