your bayonet is similar to one of the first discussed here , most likely yes it served , it would have been around in the first world war and the second as well as korea , not sure when these were surplused ,
it was made in 1906 at springfield and no they were not issued by serial number as far as we know , so unfortunately that part of its history is a mystery ,
your scabord could be one of the early M1905 versions that had a brown leater outer cover with eather a krag style metal belt hanger or refitted with a wire hanger or a later M1910 version canvas cover with a leather tip and wire hanger [this is probably what you have]these slipped over what you seem to be describeing to have ,
this is what they would look like -
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