As others mentioned it would hurt fingerprinting, test here for example: https://panopticlick.eff.org
I think by default TOR Browser doesn't allow foreign extensions (for your security). It would be possible to override this at your own peril. You could accomplish similar simply by using GNUIceCat and TOR.
My personal rant: The defaults in TOR Browser (NoScript Globally enabled) are very bad for security. - So it's up to you wether you wish to compromise security over discoverability.
