Does Firefox sync upload/sync with files from your PC?

So when i got a new PC i was downloading the programs i had on my old one, and i guess it had been awhile since i downloaded this one program which has always been virus free, so not thinking when i installed it i pressed the express install which install a PUP. Malwarebytes detected that my Profile.JS? in the Firefox directory was infected, from what i can guess when i installed this program and hit express it installed a Yahoo toolbar which made Yahoo my default search engine and i guess this updated my profile.js. Anyway i used Firefox sync and wanna know does FIrefox Sync backup or upload this Profile.JS for future use? if i sign into FIrefox sync on another pc will it get the infected profile.js also even after removing the program and deleting the infected file it came back. So now that my PC is clean fresh install will Firefox restore this infected profile.js