Yes and No. Some rimfire scopes are not built to handle much use and recoil- plainly speaking, there's a lot of less than quality built scopes out there labeled for .22lr.
Another issue that was discussed here not too long ago, was the subject of paralax. Which I believe simply boils down to clarity and dark rings observed within the scope. Rimfire scopes seem to have a paralax set for 50-75yds most commonly, whereas centerfire scopes have theirs set at 100yds. How big of an issue this is? I honestly don't know. In lean, younger, and less knowledgeable times, I have put centerfire scopes on rimfires and made do well enough.
You're not talking about using the same scope for use on two or more rifles, are you? If so, please reconsider because switching the scope between two different firearms will require a whole new sight-in/zero each time the scope is moved.
Rednecks... Keeping the woods critter-free since March 2, 1836. (TX Independence Day)
I'm going to use the words "clip" and "Long Colt" every chance I get. It grinds my gears to see new members attacked when we all know dang good and well what's being refered to.