Never known them to, though some folks report crows coming into the coops and stealing eggs...never heard of it personally in my whole life in the country. The crows and my chickens will often forage near each other here in the pasture as they are both hunting for the same foods.
Start feeding the crows....they like whole corn. I'd put up a crow feeding station of some kind for that very purpose....crows drive off hawks and are very vigilant about it, particularly if they establish a rookery in the area. In my area the neighbor baits for deer and turkey with corn and...
That is an excellent idea and really using your noggin...wish more folks could think in that abstract way to solve problems. It's a natural problem and you solved in a natural way. Kudos!