Tolkien writes, in many ways, about an ideal world, especially in the First Age. In this ideal world all "good guys" are honourable and kind hearted, and all bad guys are wikick and deceitful. Also in this ideal world a beautiful spirit goes hand in hand with a outer beautiful. If anyone in ME is ugly it is because they are ugly inside as well. So if you were somehow to strip Lúthien of her beauty, when Beren found her he would have thought she was ugly inside as well, as that is how it worked in the mythology. So the answer is no, he would not have fallen for her.
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Utúlie'n aurë! Aiya Eldalië ar Atanatári, utúlie'n aurë! The day has come! Behold people of the Eldar and Fathers of Men, the day has come!
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