Do not give out your private keys anywhere except where they're needed. They are meant to be private for a reason. If this service was serious, it'd instead rely on fingerprints (sha256/sha512) and not the key itself.
Wouldn't it being making the matter worse? You wouldn't know if it's a collision of the hash or of the keys themselves
Assuming for the sake of argument this were a real service checking for matches, the chances of a hash collision with SHA256 is effectively 0.[1] I entered the limit for BIGINT (9223372036854775807), and the approximation of the probability of a hash collision after generating 9223372036854775807 items in SHA256 is zero. The exact probability would probably take eons to calculate, but it's vanishingly close to zero.