No. In "A Good Man Goes to War", River explains to Amy that Gallifreyan won't translate. Also, there have been instances where the Doctor has been separated from the Tardis enough that the translation circuitry doesn't help him (as in "Planet of the Dead"), and he has been able to use whatever language he needed (in "Planet of the Dead", he spoke both English and the language of the Tritovores).
In various other episodes the Doctor has implied that he doesn't need the TARDIS to learn languages. Either because he has physically learned them, languages is a part of being a Time Lord or his exposure is so great he no longer needs to translation.