No they can not. When Endeavor pilots go in for an SSP interview they sign an "authorization for release of employment records related to attendance and reliability" form which allows Delta access to their personnel file. This is only for SSP interviews. Off the streets, including any Endeavor off the street, does not sign the reliability form. Therefore Delta does not have legal access to your companies personnel file.
I know an endeavor guy who talked to Delta at a job fair, he had some pretty serious disciplinary issues, Someone who works very close with AK, told him to not interview as an SSP but as an off the street hire, that way his disciplinary issues would never be looked at.