It depends on who post WWII runs for a third term. If it's Ike getting a third in 60, I think so. Otherwise, no.
Actually I doubt any president would actually have gone for a third term. Ike and Reagan were relatively old at the end of their presidencies, at least for their era. Nixon may have in 1976 without Watergate. Clinton maybe in 2000 could be the exception. Bush would have been DOA in 2008 and Obama probably had enough in 2016. Trump for certain would have in 2024, but he was aleady defeated in 2020.
Yeah I can't see Ike and Reagan run for a third term so Clinton would be the first president to do so.
Trump yeah would have run in 2024 if he won in 2020 but he would be headed for a massive defeat in this upcoming election given how badly all long time incumbents are doing all across the West currently. Polarization would prevent him from doing as bad as the UK Tories/CDN Liberals but he probably loses worse than McCain did in 2008.
So really the only elections i can realistically see someone winning a third term is 2000 and 2016 as Clinton and Obama were young enough to do so unlike Eisenhower and Reagan and more popular than W/Trump too.