No, she picked up her sudden Yo-Tourette's sometime between leaving the Hyperion Hotel and arriving in Sunnydale. Which leaves us with two options-
A) Willow picks up hitch-hikers, and they happened to drive past the Ninja Turtles.
or
B) Somewhere along the way, the real Faith stumbled across somebody who looks almost exactly like her, but with a smaller tattoo and stupider vocabulary. Deciding that she was sick of Willow's lame ass travel games, she escaped, free to murder all the low level politicians she could wish to.
"Faith. I have a plan. We need to use this Deus Ex Machina to unlock the Slayer potential of every girl possible, or we don't have chance of holding back armageddon."
"Awesome! Cowabunga!"
"Sorry, what?"
"I was jus' sayin. That's so totally radical."
"Faith? You... you're not Faith! Yo-you're just some extra from Point Break!!"
"Whoa! Don't have a cow, yo. I got Madd Skillz too!"
"Gah!"