Shmi was a slave, which is illegal in the Republic. Thus, she would be living outside the Republic, and thus Anakin wouldn't be found by the Jedi, and become a Jedi (of course, he did, which per Qui-Gon, was the will of the Force).
I believe Wookieepedia also has Plagueis dying years before Anakin was born, citing the New Essential Chronology. I suppose it's still possible if it's something that takes time for the midi-chlorians to do or whatever.
Supposing that's the case, if Plagueis didn't die, presumably he would have taken Anakin and disposed of Sidious, precluding Qui-Gon from finding Anakin.