Depends what you mean by 'right', but I'd be in favour for the following reasons:
- If you shoot them you are ridding the site of a pest which is eating your crops.
- I presume that you don't have a concience about ridding the site of other pests eg slugs - how are the pigeons different
- They are not contributing to the site (i.e. butterflies have caterpillars which eat your crop, BUT the butterfly presumably contributes by pollinating things)
- If you are eating them too they are not being 'wasted'
Can't see a downside to your plan, really