Well...
Rimfires
DO react a little bit like a springer airgun.
If you have ever fired a Marlin 60 semi auto .22 with cheapo scope mount rings, you probably noticed that the scope has a tendancy to creep towards the butt of the rifle.
It's common. There are threads right here on THR about how to make them stop doing that.
But wait! doesn't the rifle "Kick" rearward? Wouldn't inertia make the scope slide toward the muzzle?
Yes, it would. But here's the catch... The kick of the .22 bullet being fired isn't what's making the scope move. It's the slam of that heavy bolt smacking into the breech face of the barrel doing it.
See, the recoil of the bullet firing is gently absorbed by the recoil spring and the nylon buffer at the rear of the action.
The closing of the bolt, however, is tempered only by whatever resistance the cartridge offers as it goes onto the chamber. After that, it slams home so hard that slow motion videos show it bouncing as much as a quarter inch.
So, the answer is yes. A .22 auto does have a sharp forward kick.
But in reality it's nowhere near the energy levels found in a springer airgun and there are people shooting ridiculously cheap scopes on them all over the country.
I don't think you need to worry about your .22 breaking your scope.
You might want to invest in a good set of rings, but the scope will be fine.