No since the birds will drink the water. You could try and make a dust bathing area for the birds and put a mite killer in the dust. You might do a internet search for a store that specializes in birds and send them an email as to what they suggest you use.

Hoping you dont find fallen nests often, unless they are old and not being used. Mites, blowfly, etc. are common in bird nests. It's part of nature and best left alone unless you are a nestbox landlord.

Thanks for your replies. Generally, I try to keep interference to a minimum, but there are small, simple things that can enhance the chances of wildlife success. After all, the prosperity of mites is not one of my goals :).