Ugh, how would YOU answer or act in a situation like this? I did it as respect for her requested privacy. That said, what's so awkward about her parents talking to our son and me possibly hearing what they're talking about that requires me to be gone?
"I wont listen in since you are asking me not to. I am not going anywhere though."
Emphasis on she is asking you, and not telling you.
Based on past experiences, if I said something like what you suggested, i.e. "I won't listen in on the conversation", she wouldn't believe one word of it and get irate about it. I would do it, if my son wasn't a factor in this, you know? In this case, I played chicken with her and I lost.