After Neo receives his first upload of combat training, Tank paraphrases the famous line from the commercial, saying, "Hey, Mikey, I think he likes it".
This line is from a 1972 commercial which ran for 12 years in regular rotation and has been used through 1999, giving it a 28 year life span.
Morpheus states that the year was 2199 rather than 1999.
Tank was born in Zion, so the idea that he would have been exposed to commercials is not possible. The idea that this commercial and the vagueness of the Life cereal commercial would have been lost to time.
One could say the others from the Matrix could have exposed Tank to the idea of using that phrase, but it seems unlikely that Tank would have any connection to using it as a catch phrase due to the lack of exposure.