Well back when I was married to my previous husband, my boyfriend (who is now my husband) fell deeply in love with me but did not tell me because he did not think it was appropriate to do because of the perceived limitations he saw on what our relationship could be. He did not say anything to me until I told him I loved him. Have you told your girlfriend you loved her?
The only problem that would have existed would have been if he started saying he wanted to be my "primary" or to leave my husband for him. I would not have a problem with him bringing up a conversation about being as important to me as my husband/being a co-primary. I think the only down side to him or any other person in your position admitting his feelings would really be
1. to find out that it's not possible because only one primary is allowed in their current relationship structure, then you deal.
2. to find out that it's not possible because the person isn't interested in you enough to want you in their life to that depth, and then the imbalance between your feelings and their feelings could possibly lead to the end of the relationship, but it has the ability to lead to much more doesn't it?
Anyway, I would be sad if a partner I had was not upfront about their feelings. Faking that you aren't madly in love with her doesn't seem to be good for you, which therefore isn't good for your relationship, therefore it isn't good for her. Sigh, then again, I haven't risked and lost for a long long time, so it's probably easy for me to give brave advice.
Happiness will never come to those who fail to appreciate what they already have.