doubtful...
CarFax, in a word = useless.
If you see any issues listed on a CarFax (things other than title xfers, inspection/emissions annual testing, registration & occasionally basic maintenance), generally you'd be best served avoiding said car in it's entirety. In my experience, issues they catch wind of, regardless of how romanced on their report ("checked battery", "transmission maint"), are much much worse...
YMMV