Wow, so many interesting and varied responses. Thanks so much!
To those who expressed concern about DADT in general...in theory I'm okay with it. In reality, well...it just makes me worried that me and the guy might be doing things that his girlfriend wouldn't be comfortable with, but none of the parties know this because of the non-existent communication. I worry that one day everything will come into the light and cause one mess or another. Ultimately, though, it is on him to know what the agreement with his girlfriend entails, and whether or not DADT is working for their relationship. So until I definitively learn otherwise, I am working under the assumption that he is indeed being honest and faithful.
All that aside, I have a question for you. Is the relationship, as it currently exists, meeting your needs? Does it seem to be meeting the needs of the others involved? It might be that the current, ambiguous situation is viable, and that's a possibility that's at least worth contemplating a moment. Getting into polyamory for me has been about giving up the binaries and labels in thinking about people: gay/bi/straight, dating/friends, primary/secondary/tertiary. Relationship styles that are new (for me) are part of the fun.
This kind of puts words to what I've been thinking about, actually. Phrases like 'If it ain't broke, don't fix it' come to mind. I am also thinking about this feeling of 'wanting more' that seems to be creeping up on me, and I'm considering the possibility that the problem isn't with the relationship structure itself, but within the relationship as it stands. It could be as simple as the fact that we haven't had time alone in a while that is making me feel restless, especially since the relationship is so new and I want to explore it more. I think that the DADT arrangement is indeed making me a little uncomfortable, which might also be contributing.
More and more I'm thinking that I want to try to get him to, if not outright introduce his girlfriend to me, then to at least tell her about what is going on. I might start casually by asking him to show me the pictures of her that he said he was going to, and go from there. I'm interested to see if knowing that she is aware of the situation and is still okay with it might be enough to ease this feeling of dissatisfaction I'm starting to feel.
Other than that...the relationship does seem to be meeting my needs, I think. I'm getting affection, intimacy, emotional support, and companionship. What I'm not getting boils down to mostly time commitment and official 'couple status'. The status part I could care less about, because the relationship itself is more important to me than how it's defined. As for the lack of time commitment...it bothers me to an extent until I realize that it goes both ways, and that I would be expected to commit some of my time as well. Having just gotten out of a long relationship and going through the process of rediscovering myself, I'm not sure I would want social demands put on me at this point.
I guess I'm answering my own questions after all, which I knew I would have to do in the end.
But just putting my thoughts out there and reading everyone's responses has really helped me to start to bring my feelings to the surface and organize them a little bit. So thank you everyone!
I will see if I can't gently nudge this guy towards talking to his girlfriend about our situation. If anything comes of it, I'll be sure to come back here and let you guys know.
edit: I forgot that I wanted to address this comment by redpepper:
I haven't really gotten how that all works when someone thinks that if they don't know what their partner is doing then they won't be replaced
I think I may have been a bit unclear at some point. The girlfriend's fear of being replaced seems to be the reason for restricting committed, romantic relationships outside of their relationship. It does not seem to be the reason for DADT in this case. What their reasons are for deciding on DADT I can only speculate about, though I do hope that the reasons are healthy ones for their relationship.