This is a non-issue for several reasons, among them:
1) Covert officers travel under diplomatic cover, and most diplomats have security clearances. This will not stand out.
2) It's already trivial for a nation-state to identify spies under diplomatic cover. We know who theirs are, and they know who ours are. Diplomatic cover is not about cover; it's about *diplomatic immunity*, so if they get pissed at our spies, all they can do is kick them out, and vice versa.
3) Non-official cover employees are harder to detect, but they generally only hide their present employment, not their past employment, and usually have cover stories, not cover identities/jobs. See: Valerie Plame. At best, you can use fingerprints to confirm that they are who they say they are, which they're not lying about anyway, so...
The real danger is blackmail. The employer already knows what infractions are listed on the SF86, of course, but the general public may not. Affairs, drug usage, and to a lesser degree, expunged criminal history, arrest record, financial issues, etc. Just download an SF86 and look it over. Depending on the individual, it could be a scandal that they'd rather avoid, and/or that the employer would rather avoid. e.g., "Why would you hire someone who smoked crack?"