Try it and see! Tor Browser contains modifications specifically to make fingerprinting harder. Panopticlick gets 11.36 bits of information from Tor Browser on my computer, compared to 22.16 bits from unmodified Firefox on the same machine. With Tor, Panopticlick says "Within our dataset of several million visitors, only one in 2,620 browsers have the same fingerprint as yours."
That said, browser fingerprinting is very hard to fight, and it's a lot easier to come up with new fingerprinting techniques than it is to mitigate them. So I expect that determined fingerprinters have the edge in this arms race.
That said, browser fingerprinting is very hard to fight, and it's a lot easier to come up with new fingerprinting techniques than it is to mitigate them. So I expect that determined fingerprinters have the edge in this arms race.