Essentially, in order to answer this question, you need to realize what, exactly, your goals are. For instance, if your audience will be inserting themselves into the main character's shoes, and this is the main purpose of the book, then, yes, the love interest character does need to be sexy. If your goal is to write a vaguely disgusting scene demonstrating the depravity of the society of your novel, or some such, then an utterly repulsive character would serve.
However, the general purpose is to create a realistic romance. So, I would argue that the love interest characters do need to be sexy, in the main character's perception. If it is realistic and in-character for your narrator to fall for her cuddly, pudgy nerd of a best friend, and you can make the reader believe it, then by all means, go for it. It'd make a refreshingly different story, and a far more realistic one than many that are out there. However, bear in mind that, in real life, the vast majority of people, like it or not, do judge by appearances, at least to some degree. If this girl is going to fall for the less-than-conventionally-perfect, just make her tastes less than conventional. Have her notice the good points that others might not, and the readers will see it, too. Maybe she focuses her friend's gorgeous smile, on her bright, intelligent eyes, on the secure, independent way she carries herself.
If the physical descriptions are like that, we'll see why she's head over heels. But if all we see is the friend's dorky clothes, unkempt hair, and chubbiness, then, no matter how much the narrator dismisses them as unimportant quirks, the romance will be unbelievable, not because we doubt she would fall for her if she looks like that, but because we doubt that, if the character truly is falling for her, she would look at her like that. Why? Because, generally, romantic attraction tends to be coupled with physical attraction, and, except in cases where physical attraction really isn't a component on any level (as in, the relationship is purely an intellectual/emotional/romantic one, and nothing else, and not developing into anything else, however small or innocent), it feels unnatural for a character to state that (s)he is attracted to someone and yet be unable to focus on anything but his/her dorky glasses, clammy hands, and lacking physique.
To make a long post short, love interest characters may not be conventionally "sexy", but they should become physically appealing in the narrator's and, unless you're intentionally going for dissonance, the reader's perceptions, or the emotional attraction will feel weirdly isolated.