The Mishnah was compiled around 200 CE. (see Wikipedia)
This date is also given in the books i checked (the Steinsaltz reference guide, Aryeh Carmel's Aiding Talmud Study, ArtScroll's history book).
According to those books, Rebbe ascended to the position of Nasi in around 170 CE. Wikipedia gives his birthday as 135 CE. This would put him at 35 years old taking office, and 65 when he compiled the Mishnah. Again according to Wikipedia, he died at around 217 CE. This would give him another ~15 years to have changed his mind.
However, the Steinsaltz reference guide says he held office from 170-200. This would seem to indicate that he died shortly after completing it.
Aiding Talmud Study indicates that Rebbe's son, Rabban Gamliel III, took office at around 210 CE, between Steinsaltz and Wikipedia.
Wikipedia has a source; the books don't.
So, it depends whose dates you take. He might have had time, or maybe he didn't.