"Would it be a tactical error for him to point that out when asked?"
Yes, in fact, it would. You'll note that in public at least, Barack Obama has kept his mouth tight shut on the subject of black voters defecting or staying home if he doesn't win the nomination, even though it would be a powerful counter to Clinton's talk of "hard-working white Americans" who won't support him. And the reason he's keeping his mouth tight shut is that he knows the danger of splitting up the Democratic base along racial lines. He doesn't want to say anything that's going to feed into that.
When anybody asks Obama a question along those lines, he talks about how he's confident he'll be able to pull everybody together, which is just what he ought to talk about. And yes, that one guy in his campaign who said working-class whites go to Republicans every election was making a serious blunder, even though what he said was also true.
A Democratic candidate who wants to win in November needs the whole Democratic coalition behind him/her--black voters, Democratic working-class white voters, and latte-sipping liberal elites like me (okay, I don't actually drink latte and my elite credentials are limited to a bachelor's degree and a white-collar job, but I do tend to identify with the academics). Concentrating on working-class whites to the exclusion of the other groups is a dangerous game.