It wouldn't really matter much, as a number of the main organizers for George Wallace's campaign in '72 were willing to either participate in his run for the Democratic nomination or revive the American Independent brand, but not both. Doing that would also have raised serious issues as to ballot access given he would have participated in a number of Democratic primary races and been denied general election ballot access (which he could fight, but would have sucked up a lot of funds doing so with no guarantee of winning), and it may well have damaged his performance overall in both the primaries and the general, leaving him a still considerable if weaker presence overall.
I think it goes without saying that like other American third parties (Free Soil, Reform), Wallace's party would get substantially less support the second time around if he were to give it another go. Even had Nixon decided to run as a liberal on civil rights, his law & order message and the War on Drugs were going to sap up Wallace's support no matter what. Combine that with his OTL Southern Strategy and that's even more true come 1972 if Wallace goes third party. I imagine that Wallace would win at least two or three states, but he'd get much less support this time around. Maybe 7-8% of the popular vote versus the 13.5% he got in 1968.