Hmmm. Since the EvE servers can reliably link accounts to specific persons or computers (either by shared EMail addresses or a machine identifier) it is possible to add a block function like “Block this and other (future) accounts from this person”.
The receivers don’t even need to see the identifying feature of the sender’s account, on client side there may just be a SHA256 hash saved of said feature which has been generated when the client asked to block this character and its associates. On loading new character data (like, the portrait), the client would send the hash back to the server, server would compare and then report back to the client if the sender would have to be blacklisted or not.
Given this, the only way to circumvent that block would be to use throwaway email addresses (easy enough) and use different machines or completely wipe and reinstall EvE (though, the latter might not even work if the machine identifier is completely based on the underlying hardware).
So it is technically feasible, even rather easy to implement and with little overhead, and that without passing along sensitive information.