No.
The one time that the question of an Anti-War candidate was polled, with McCarthy as the stand-in before the shock of his performance in New Hampshire, he net around (12%) of the vote nationally; predictably a Peace Ticket was strongest in the Northeast and the West. The problem lies in that there is no incentive for a Peace Ticket to form early when you have candidates like Kennedy and McCarthy competing for the Democratic nomination and walloping the Johnson and Humphrey stand-ins, and it is a mite too late by the end of the Democratic National Convention when the anger of the nomination having been "stolen" was at its fever pitch. This isn't to say that McCarthy couldn't have run as an Independent in the election, there was a lot of movement on the ground to that effect among his supporters and they were putting him on the ballot in places, but there is nothing to prevent Humphrey or Johnson from coopting the momentum of McCarthy's candidacy by announcing a halt to the bombing or a peace initiative with North Vietnam. Under those kind of circumstances, even if McCarthy were performing particularly well, his support would start to bolt back into the Democratic camp.
McGovern for his part endorsed Humphrey at the Convention itself, and breaking so openly with the Democratic Party would have seriously jeopardized his bid for reelection in South Dakota that year; I actually am not sure if South Dakota has something akin to the law that allowed LBJ to run for both President and the Senate, and if push came to shove he would have remained in the Senate. John Lindsay on the other hand was still being considered in some quarters as a possible successor to Nelson Rockefeller within the New York GOP alongside Senator Jacob Javits, and maintained close relations with the Nixon campaign throughout the year.
The issues with McCarthy running as a Peace Candidate can also be highlighted by the opinions of some of his strongest backers, like Senatorial candidate Paul O'Dwyer who was wholly opposed to the Humphrey campaign and wanted nothing to do with it even after its victory in Chicago; he believed that a "fourth party candidacy" was simply not tenable, and that all efforts should instead be expended backing Peace Candidates in the House and Senate Elections across the country. I suppose another way to think of it would be to compare it to the reaction Teddy Roosevelt got when he bolted the Republican Party when he lost it's nomination in 1912, with many of his strongest supporters in the Republican Party refusing to bolt alongside him, opting instead to abstain from the conflict or throwing their support to Taft.
I suppose a comparison to the Progressive Party is somewhat valid as the New Party (it was actually going to be called "New Party"), was set to run candidates for all offices alongside McCarthy Presidential campaign, and subsequently shriveled and died once McCarthy came too and began shooting off telegrams asking that his name be withdrawn from the State ballots. The New Party's death did not happen all at once, but its core was within the Academic Community with fairly few members that were grounded in the reality of politics, meaning that the means for it to grow without McCarthy's presence simply wasn't there.
Now in terms of who'd be running with McCarthy in this hypothetical scenario, well that rooster is actually quite small. The one ballot that actually listed a running-mate for McCarthy had opted for Mayor Lindsey, but I've mentioned above why he'd have shied away from associating himself with the Peace Campaign. Julian Bond was another major backer that was never enthusiastic about Humphrey that year, but he is ineligible. Smaller names that have come up are James Hormel, who was at that point recently the Dean of Students at Chicago Law School and later be named by Bill Clinton as the Ambassador to Luxembourg, and Marcus Raskin who headed the Progressive think tank known as the "Institute for Policy Studies". I suppose Doctor Benjamin Spock also deserves a mention given his popularity among Leftist circles, but it would be a fairly controversial choice as well.
