Interesting idea. Think it would fire up some part of the base, but the media would go 24/7 on Gingrich negative stories. OTOH Gingrich can be effective...when he stays on message.
The negatives are ancient history because of all the personal and spiritual changes Newt has made, leaving now a very tough case for negatives to make.
There are the small group of the sinless, of course, who like to role Newt’s past personal misfortunes around in their fingers, but that says much more about them than anything of his historic accomplishment for the Republican Party, for which he crawled through glass to turn around.
As a party we are indebted to Newt for his genius and his toughness, but some prefer to lay stripes forever over periphreal issues.