I BELIEVE you could make it work. Since most .22 conversions have a stationary slide and only a small portion to the rear of the conversion unit moves back to extract the spent casing.
I'm not familiar enough with the units to know 100%.
I'd be inclined to say that, yes, it would function, but it wouldn't be pretty, what with the gap between the dustcover and all.
As for getting a conversion, you could spend just about as much and get a whole new .22 1911 that would be more inclined to work since it was designed around the rimfire round to begin with.
Most 1911's come with a ~21 lb mainspring from the factory. It requires a pretty good bit of momentum to bring the hammer back, which still has to happen with a conversion top-end. A lot of guys are having trouble with the conversion units functioning well.
My two cents.