If a non-Jew touches uncooked wine it is considered yayin nesech. If that same non-Jew then converts and states categorically that he did not offer the wine as an idolatrous libation when he was a non-Jew, may he, or another Jew, drink the wine?
A similar question applies to food cooked by a non-Jew who is converting to Judaism--can the convert eat the food or is it prohibited as bishul nokhri? R. Herschel Schachter apparently holds that the convert may eat the food he previously cooked as a non-Jew, for the following reason: There is a question whether the prohibition is based on fear of intermarriage, or possible violation of kashrut. Regardless, the reason does not apply in this case, as the gentile no longer exists and he also knows whether there is any non-kosher food. In this case, we can likewise argue that whether the prohibition is based on intermarriage or concern that the wine was used for idolatry, there is no problem.
In fact, this is an explicit Yerushalmi (Eiruvin 9:4): גר שנתגייר והיו לו יינות ואמר ברי לי שלא נתנסך מהן בזמן שנעשו על גב עצמן טהורים לו וטמאים לאחרים -- According to the Yerushalmi, as long as he is the only one who touched the wine he is allowed to drink it but no one else can.