Is it possible to validate an email address without the user actually revealing the email address? Say hypothetically I want a service where users express their opinions. But those opinions are heavily dependent upon where they work, and the best way to prove that they actually work at a specific place is by having access to an email address there. However, the service must guarantee that it (or anyone other entity) cannot know the user's specific email address, or else the user won't express their honest opinions. 

Is this do-able? 

So say I work at companyx, and my email is bob@companyx.com. When I sign up for this service, the service needs me to prove that I have access to a valid, current email address at the companyx.com domain. However I do not want to type in anywhere that my email is "bob@companyx.com" because then the service would know that I own that specific address. The service does not care that I specifically own "bob@companyx.com", just that I own some valid address at "companyx.com".
Your idea is exactly what is achieved in a recent paper:


  Blind Certificate Authorities.  Liang Wang, Gilad Asharov, Rafael Pass, Thomas Ristenpart, abhi shelat. At IEEE S&amp;P 2018.


The server and client use secure multiparty computation to jointly make an SMTP+TLS connection to a mailserver, generating the appropriate encrypted packets to send an email to username@domain.com, so that the server doesn't learn username and the client doesn't learn the random challenge in the body of the email.