Seriously? Seems like he'd have to take a hard look at Skye's (lack of) professionalism first...that's what May was taking her to task for, and rightly so. If Skye really wants to be a SHIELD agent, and isn't just there to find out about her parents, then she needs to straighten her priorities and get her head in the game.I can't see Coulson not looking into that further for reasons of personal ethics, operational cohesion, and so on. Especially if he overheard what May said.
On the other hand, Coulson is the one who is stringing Skye along, pretending to help her on her quest while hiding the truth from her--and now he's enlisted May to string Skye along as well. Maybe they should just level with Skye and tell her, "Sorry. You don't get to know that. End of story."
One can hardly blame Skye for obsessing over her quest when they keep tossing her breadcrumbs . . . while keeping the answers dangling just beyond her reach.