It will be curious to see how long it lasts.
When we moved here 53 years ago the crows routinely knocked the lid off the garbage can and strewed trash around the yard. I padded the jaws of a jump trap and set it on top of the garbage. Early next morning pluperfect heck broke loose - I caught a crow. Every crow in the neighborhood was circling and screaming in anger. When I came outside they left. I eventually let the crow go, and there's never been a problem since. Crows educate one another on what is 'bad'.
For the OP shooting one crow and leaving it visible in your yard will cause all crows to stay away for a long time.