Short answer: Very probably not.
Longer answer: Almost certainly not if the candidate is Mitt Romney. Romney served one term as governor of Massachusetts and was not popular at the time he left office. A Survey USA poll conducted in mid-November 2006 put the outgoing governor's approval rating at just 34 percent, against 65 percent disapproval. This poll does not particularly seem to have been an outlier. A Boston Globe/University of New Hampshire poll in late October, 2006 also had Romney's approval numbers in the red -- 34 percent of likely voters had a favorable impression of him and 54 percent an unfavorable one -- and polling conducted throughout 2005 (before Romney announced in December of that year that he would not seek a second term) showed him as many as 16 points behind his prospective Democratic rivals. Voters had evidently had enough of the guy.
But wait -- it gets worse. Voters not infrequently cross party lines to vote for governor -- 18 of the 50 states (36%) currently have a different party representing them in the governor's mansion than the one they cast their vote for toward the Presidency last November. But that's true for just 22 of 100 Senators. Voters recognize that Senate is a national office and governor is a local one: they're less likely to vote for a Senate candidate from the "wrong" party since they know that, once he gets to Washington, he'll be under enormous pressure to toe the party line, in a way that a governor who is not part of a larger constituent body might not be. Yes, quite a few people have made the cross-over before, including some in unfriendly territory (Ben Nelson of Nebraska is one case in point). But these instances are becoming rarer as the partisan divide in the country grows more extreme. And that would seem particularly to be the case for a candidate whose only reason to run for the Senate would be to help him defeat a Democrat for the Presidency in 2012 or 2016.
Plus, there's the question of how Romney would position himself. Is he going to revert back to being pro-choice, and pro-civil unions again? He probably can't win the Senate seat unless he does. But he probably can't win the Republican Presidential primary unless he doesn't -- particularly on the abortion issue. While I think it would behoove Romney to run slightly further to his left than he did in 2008 -- a lot of conservatives aren't going to vote for him anyway between his religious affiliation and the likely presence of Sarah Palin in the Republican primaries -- that would be taking things to extremes.
Speculation aside, Mitt Romney is probably smart enough to know this (whatever else you might say about him, Romney's not lacking for brainpower). Romney has a pretty good brand and probably 75 percent-plus name recognition among likely voters. And last I checked, you don't have to be popular in Massachusetts to become elected President. Running for the Senate seat is virtually a pure downside play for him.
As for other Republicans in Massachusetts, their prospects don't figure to be much better. This is mostly because there aren't very many of them. Something like 40 percent of U.S. Senators had been U.S. Representatives at the time of their election -- but all 10 of Massachusetts' U.S. Reps are Democrats. Statewide office holders like Lieutenant Governors and Attorney Generals have also had their share of success when running for Senate -- but Massachusetts' A.G., Lieutenant Governor, Secretary of State and State Auditor are all Democrats. State Treasurer Timothy Cahill is a Democrat-turned-independent, but he's expected to run for governor instead. This, incidentally, is another layer of protection that the Democrats have -- any Republican worth his salt should be trying to knock off the unpopular Deval Patrick, rather than trying to win Ted Kennedy's old seat. Unless William Weld is interested -- and Weld endorsed Barack Obama and might vote with the President anyway on issues like health care and cap-and-trade -- this one is probably a pipe dream for Republicans.
Short answer: Very probably not.