Heero Yuy NWZC
Preventer Void
Sorry, I just can't see it. It would take something extremely severe to get Relena away from Heero, and Duo, though flirty, seems to acknowledge the attraction and even encourage it. If that extreme thing happened, I could more easily see him trying to help a reconciliation than scoring her on the rebound. Besides, Duo seems like the sort of guy who wouldn't do that anyway; he'd probably consider it a betrayal of trust to go after a friend's ex.
I don't think it's a patience issue... but more of a respect issue. Duo would understand that she's got her job and all that, and that would be the end of it. Besides, Duo's always been the underdog. I think that, after a while as tagging along as the Vice-Foreign Minister's low-class boy-toy, he might get tired of the ettiquette garbage and bail... partially because he's not the hoity toity typ and partially because he might end up just feeling outclassed and annoyed by the people she would be spending time with (former nobles, politicians, high society, papparazi).