But the employer would, because the firm they use to do background checks will use an IP in the States to do the search.
USA privacy laws are bad enough you can get sicced by a private investigator most of the time with no questions asked, no repercussions.
They would, of course. Unless, someone's planning to build a whole Chinese-style censorship state, it's not possible to disallow to obtain information through VPN.
I've never encountered one in Germany and we certainly don't do them with potential applicants at my place of employment. (No idea whether this is because of a law or for different reasons)