In VA, the Federalists did run a separate ticket--which predictably lost overwhelmingly. Even an attempt to run an uncommitted Federalist slate which might attract Clinton supporters narrowly failed, and Virginia Federalists insisted on supporting a strictly Federalist ticket--Rufus King of New York and William R. Davie of South Carolina (formerly governor of North Carolina). What turned even the most sympathetic Virginia Federalists against Clinton was reading "the address of the New York Clinton committee, which praised Jefferson, urged a vigorous war against Britain, and demanded territorial gains for the United States." As one delegate remarked, 'It promises nothing but the gratification of New York as a reward for our exertions to elect Mr. Clinton."
https://books.google.com/books?id=agYzhC6LyJEC&pg=PA146 The King-Davie electors got 27 percent of the vote--which at least is slightly better than Adams did in VA in 1800... No doubt Marshall, had he been willing to run, would have done better than King in VA, but he would still have easily been defeated.
Anyway, no Federalist candidate would have the slightest chance without New York--but even with New York (which Clinton carried) their chances were dim. It is often observed that Clinton could have won if he had carried PA--but the trouble with this is that PA was not at all close, going for Madison over Clinton by 62.6-37.4%.
http://staffweb.wilkes.edu/harold.cox/pres/PaPres1812.html Clinton carried only a handful of Federalist-leaning counties in the southeastern part of the state. A "real" Federalist would probably have done even worse in PA than Clinton did.
Basically a "true" Federalist candidate would have had all the weaknesses of Clinton without his New York base of support. True, if the candidate was Marshall, he might have done a little bit better than Clinton did in the South, but that just means he would have been defeated a little less overwhelmingly there. In South Carolina, once a Federalist stronghold, there is a good discussion of 1812 in James H. Broussard, *The Southern Federalists, 1800-1816,* pp. 151-153. "Inasmuch as the Federalists had steadily lost ground since 1800 and now held only about ten percent of the legislative seats, no one expected anything but a substantial Madison victory in 1812."
https://books.google.com/books?id=agYzhC6LyJEC&pg=PA151 To make matters worse the legislature had recently been reapportioned to give more seats to the upcountry, where Federalists were weakest. Even in the low country, the Federalists were weakened by the extension of suffrage to all white adult males. The Federalists did put up a spirited campaign in Charleston, but lost even there. The result was that the Assembly elected in 1812 was even more Republican than its predecessor, and so nobody even bothered to put up a Clinton slate of electors; the legislature chose a Madison slate without opposition. In North Carolina, it was thought there was a chance of some Republicans voting for Clinton because of resentment of the North Carolina legislature's decision in 1811 to abolish the district-election system for voting for president and to substitute election by the state legislature.(which everyone knew guaranteed Madison getting all the state's electoral votes). Resentment of this led to gains in the August 1812 state legislative elections by Federalists and also by Republicans opposed to the change. "A distraught Republican feared that resentment against the electoral law had split his party so badly that Clinton would carry off the honors in the presidential voting."
https://books.google.com/books?id=agYzhC6LyJEC&pg=PA149 However, "More sober heads, mulling the returns, realized that some legislators who opposed the electoral law would not necessarily support Clinton for president. Peter Browne, a Halifax Federalist, admitted that, despite his party's legislative gains, there was still a clear Republican majority, at least on the question of Madison's reelection. .."
https://books.google.com/books?id=agYzhC6LyJEC&pg=PA150 The governor refused to call a special session of the legislature to reinstate electoral districts. When the legislature did meet in its usual end-of-the-year session, it first narrowly refused to reinstate electoral districts and then proceeded to choose electors: "After much canvassing and wheedling, the Republicans held a caucus to whip their forces into line, and the Madison ticket triumphed by the huge margin of 130 to 60. No Republicans deserted their candidate, and even a few Federalist members forgot Clinton and instead voted for the very president their party leaders had been denouncing for years as a bumbler and a tool of France."
https://books.google.com/books?id=agYzhC6LyJEC&pg=PA151 Marshall might not have lost NC by such a huge margin, but he would still have lost.