I was told by VS employees at LHR that we were not eligible and even they don’t get to fly up front on the TA routes. I think it’s their “upper class” that is equivalent to DL One. She told me that they can get the Premium Economy or Economy only.
Update: I got a few different answers when I flew, but it seems that Delta non-revs are not eligible for first class. Very cool airline, though. What’s also GREAT about Virgin Atlantic for nonrevs? If there are plenty of seats they will just print your ticket with an assigned seat when you check in, no need to worry up until boarding time. (Well sometimes you may need to, but not if there are plenty of seats versus just a few.)
Leaving my city I had to wait, didn’t see how I was supposed to know when I got a seat and they weren’t calling people, so I politely asked at the desk and they gave me a ticket. But leaving London they told me the seats for my flight weren’t great and weren’t sure if I could get on, but were able to give me a confirmed seat to the closest big city in my area immediately which was a huge relief, and I was able to take a quick Delta flight home from there.