Clay most likely will not remove the paint damage that the bird poop has etched into your paint. Clay only removes above surface contaminants, anything that has bit into the top coat in not removable with clay.
Depending on the severity of the etching, take the least aggresive approach to a cleaner/polish first. Then work up to more aggressive if the least fails to remove the stain.
Due to the acidity that these birds have in their digestive systems to eat just about anything, the results are sometimes extensive paint damage from this dropping. Sometimes color sanding may be even necessary to completely remove the defect, and then polish it up.........
But again, take the least aggressive approach first always!
Dave @ Innovative Detailing