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No a kohen is not allowed to perform birkat kohanim if he is married to a convert or even if he is no longer married to one until he swears not to do it again as the shulchan aruch paskens in OC 128:40, "כהן שנשא גרושה לא ישא את כפיו ואין נוהגין בו קדושה אפי' לקרות בתורה ראשון ואפילו גרשה או מתה פסול עד שידור הנאה על דעת רבים מהנשים שהוא אסור בהם:

A kohen that married a divorcée may not perform the priestly blessing, and we do not treat him with sanctification, even to call him up to the Torah first. And even if he divorced her or she dies, he is invalid [as a kohen] until he swears off all benefit, in the public's discretion, from women who are forbidden to him."