I don't see how a segregationist party could have held onto relevancy past the 70s. Integration nationalized the political discourse around race. I think it was inevitable that the south's politics would nationalize as well. I interpret the AIP as an attempt to create a new "southern party" to replace the old Dixiecrats. Thus, with the passage of the Voting Rights Act in 1965, I just do not see how such a party could be sustained; that was the death knell of the era of a single "southern party."
One would wonder how Lester Maddox would have fared had he had a full-bore campaign on the American Independent Party in 1972.
I tend to think very poorly. One problem is that Lester Maddox was nowhere near as charismatic as George Wallace on the stump. The other is that the 1968 Wallace appeal in the South was due, in part, to the perception that there was "Not a Dime's Worth of Difference" between the two major parties. That perception of 1968 did not make it into 1972; Nixon vs. McGovern was one of the clearest choices in Presidential candidates in some time (other than Goldwater-LBJ) and Nixon was seen by Southerners who was conservative in the ways that mattered to them. By 1972, the entire South (save Alabama) had elected Governors who were conservatives (by national standards), but who were going to usher in integration because it was the law. (Maddox, oddly enough, did a LOT of heavy lifting in integrating Georgia State Government, including the Highway Patrol and the GBI; he was a racist, but he did more integrating of Georgia's government than the more moderate Carl Sanders.)
The issue is whether or not Maddox might have swung a state to a Democrat in a 3 way race. To me, that answer is a fat "NO!".