As we get close to learning who the mole is, I followed @kate-dammit-run 's lead and re-visited this possibly crucial scene from Episode 1 (Woe Has Joined).
First we have a visibly excited Dr. Borden. He can't wait to tell Mayfair about the discovery of the ZIP in Jane Doe's body. He hasn't even noticed Weller. He draws breath to launch into his astonishing news, only to be interrupted by Mayfair's introduction of the man she has brought with her.
Kurt's response to the introduction is a polite but not very interested nod. A kind of "Uh-huh, so what?" He hasn't a clue what's going on.
Then we get the "Oh, you're...wow" reaction from Borden on learning that THIS is Kurt Weller. This could either mean that he's been prepped by Sandstorm of the role Special Agent Weller is about to play in their plot, or - more likely - merely that his brain is processing the link between the tattoo prominently displayed on Jane's back and the man himself.
Borden then launches immediately into the tox screen announcement, as if he was temporarily distracted by the Kurt Weller revelation and then remembered what was so pressing that he had to tell Mayfair. He is as excited as a kid in a candy store.
Borden's behaviour persuades me that he was ignorant of Jane's memory wipe until the tox results came back. And I don't think we can read any more into his reaction to Weller than that of a surprised man making the connection with the tattoo.
When Shepherd and Roman talk about it being time to activate their mole within the FBI, it suggests that that person has not played a part in Jane Doe's deception up to that point. If Borden were working for Sandstorm and they pulled strings to have him brought in by the FBI as a consultant psychologist, he would have had to have been in on Jane's real identity and their plans for Weller from the start. It is hard to see how he could have kept up the pretence without having had his own memories blocked to some extent.
I do hope it's not Borden. He and Patterson make the sweetest of couples. She would be devastated if he were to be the one to betray her and her friends.