Do they offer any benefits at all to the security of key distribution?
Public key servers are not meant to bring security; they are meant to make the public keys available. Security is achieved, in the case of PGP, through the Web of Trust: signatures from people on other people's keys. A public key server is simply a repository so that you may more easily find intermediate public keys with signatures between yours and that of the intended recipient.
A public key is not deemed secure because you just downloaded it from a key server; key servers have no idea whether the keys they contain are genuine or not. A public key is deemed correct because you could verify sufficiently many chains of signed keys from your own key to that key. How you obtained the keys is not important; they could have come over some HTTP connection, on USB keys, on magnetic tapes carried by camels through the Australian desert, that does not matter. A public key server is thus just a huge camel.
Without the key servers, each PGP user would have, when he sends a signed email, to send along with it a bunch of other signed keys so that the recipient may validate the signature. This would be cumbersome and does not map well to the WoT structure. With a more centralized PKI, like the prevalent model in X.509, sending "helper certificates" is workable; that's what SSL servers do: when a SSL server sends to a connecting client its certificate, it actually sends a certificate chain.