Yes, the translation of tauba as 'repent' (to faith) can hold true as well, bearing in mind the verse 49:14 which I mentioned by number. To quote in full:
The Bedouins say, “We have attained belief.” Say (O Prophet), “You have not yet attained belief, but rather say, ‘We have submitted (to the System)’, for the Faith has not yet entered your hearts. Yet, if you obey Allah and His Messenger, He will not diminish (the reward of) any of your works. Verily, Allah is Forgiving, Merciful.” (49:14, QXP)
Nevertheless, as confirmed in the same verse, the primary meaning of 'Muslim' is 'submit to the system' rather than 'person with eiman'.