It is authoritatively debunked in Sid Meier's (excellent) memoir - there was no such integer underflow bug in Civ I, it was all a rumor that went viral. The franchise did embrace the meme, though.
I am aware that it's in his memoir, but I am not sure whether he actually went through the code to write it or just went back through his notes/memory. Or whether 2K told him to "debunk" it so he wrote some fiction (also a possibility - see Feynman's memoirs which have quite a bit of fiction in them). It was a long time ago and prior to the memoir, neither he nor any of the other developers on a Civ franchise remembered whether there was an error, and they all said as much on the record. Also, the story of an underflow was about Civ II, not Civ I. I am not necessarily convinced there is no underflow, but I am convinced that there is a plausible alternative theory.