True they may eat the hay leaves......but some straw(depending on how it's processed) can have a lot of residual grains that'll have them digging thru the nest bedding, had a batch like that here....nests torn up and oats growing in the garden where I used it as mulchHay is feed and may have tasty seeds or leaves and might encourage chickens scratching through it to find that
This is why I buy straw in the late summer/fall when it's just been harvested...if straw has been stored in a barn for months where wild birds can get to it , it's more likely to bring mites in with it.Straw can also harbor mites more easily, if you ever have a breakout of them.