Earlier quoted context omitted.
It's not real, but it's still a fine story.
How do you know?
Snopes covered this one and they cite to an urban legends book from 1989: "Curses, Broiled Again" by Jan Harold Brunvand. Brunvand prints the "vanilla takes longer" version and reports also having a "pistachio takes longer" version printed in a magazine in 1978, which itself referred to another magazine as its source. In the book's version it's a Texas car dealer who's looking into the problem. The same author's later book from 1999 covers the story again and includes versions dating back further, plus a 1992 version which is this one where it's Pontiac and the problem is the vanilla being in a separate case at the front of the store.
In the Pontiac version you can go and pick at various implausible details stacked up together, that Pontiac's president cares enough to send an engineer out, that the engineer is there when the car won't start on the first night but still just comes back many more times rather than looking at the car or presumably noticing that it starts a couple minutes later, that this guy is buying a new container of ice cream every night and never stocking up, that he never takes any other trip where it's a short stop... You can go on each of those and say they do happen: like presidents and CEOs do sometimes go digging deep on random problems customers put in front of them. But if you look at the whole thing I think you need to recognize it as a piece of storytelling, not fact.
Maybe there's some kernel of a true story in there, but if so it's probably a pretty small kernel. Anyway it doesn't matter much: it's just a fun story that teaches a little lesson so people like to share it around.