Easy answer? Yes, of course he will. Just as Ronald Reagan survived his divorce problem, George W. Bush survived his alcohol problem, and John McCain survived his "maverick" problem.
I've made this point before -- indeed, I make it all the time -- but partisanship and interest-group loyalty go a long way toward explaining political realities. If Newt Gingrich can rally the support of party elites and important interest groups, then it won't take much to convince primary voters of his worthiness. And if Gingrich becomes the nominee, then the combination of money, media exposure, and partisanship will virtually ensure his strong support from the vast majority of the Republican Party, their previous feelings notwithstanding.
The problem for Newt Gingrich isn't his infidelity; it's everything else. Gingrich is stunningly unpopular with the public at large, which probably carries over to local and state elites, given the extent to which he drove the late '90s backlash against the GOP. A few gullible Beltway elites notwithstanding, Gingrich doesn't have much of a constituency. He might have some cache with national elites, but he's stunningly unpopular with the public at large. And indeed, this is to say nothing of his transparent hucksterism: Since leaving office, Gingrich has practically devoted his life to making money in the shadiest way possible.
If Gingrich is serious about running for president, then serial adultery is the least of his worries. As it stands, this isn't even close to serious; Gingrich has been "exploring" a presidential bid for nearly 15 years. If he wanted to run, he would have done so by now. But the media is a willing player in this charade, and as long as that's true, he'll continue to weigh his options and play the press for dupes. For now, however, my guess is he that "drops out" as soon as he meets his "fundraising" targets.