He wouldn't have a chance in hell of winning. Especially if he was a one term Democratic Governor of Massachussetts. Maybe Democratic Governor of Utah or something, than slightly a greater chance. If Romney were a Democrat, the only primary he'd likely win would be Utah.
The Utah Democrats are mostly non-Mormons: those who've left the faith or are descended from non-Mormons.
He'd be a better candidate than John Kerry was simply because he's a better speaker, better looking, and a Governor rather than a Senator, but he'd still suffer from the burden of public stupidity as a Democrat from Massachusetts. He'd probably come in third in the Democratic primary, beating Edwards and Richardson but losing to Obama and Clinton. In the general election, he would beat his Republican self and maybe Fred Thompson but lose to John McCain and Rudy Giuliani.
Finally: "If Mitt Romney
Were a Democrat".