Is being a member of TER enough validate my identity with an agency? Or must I provide more information about myself, which I have no problem doing.

Most agencies like to do their own screening normally through employment verification.  In the past, some agencies has used RER membership if you have reviews

At best, being a member of TER validates you as someone who has an e-mail account.  Being white listed and having a review history is very helpful but goes no where near validating your  identity.  Screening isn't just to be sure you're not LE, it's to try and manage our risk of getting hurt and wasting our time as well.

We are all anonymous here so it stands to reason that any agency or indie looking for valid information on a potential client would not find much of use in a TER handle.  It may lend some validity if you have been around a while and have a good reputation in the TER community but that's about all.  

I've never even been asked if I was a member of TER by any agency.