Answer

In my opinion, definitely yes. A relationship with a person, or with a woman, is formed through their outward appearances and external characteristics, but through them you create a connection with the person himself or herself (the one who possesses those traits). That connection does not have to be based on self-interest. In fact, a connection for the sake of self-interest does not deserve to be called love; it is desire. (That is what you wrote: that something about her draws you. That is desire, not love.) By definition, love is a connection without self-interest. This is discussed at length by Don Judah Abravanel in Dialogues of Love, and by José Ortega y Gasset in On Love: Five Essays. This also resolves what the commentators asked about our forefather Jacob: "and they seemed to him but a few days because of his love for her." Normally, if you love someone, every day seems like an eternity, yet here it says the opposite. The answer is: that is true when a person desires someone, meaning he wants to attain that person, and that means he loves himself. But Jacob loved Rachel, not himself.
See also my column 120 on altruistic acts, which is related to this.
I do not know whether this is what you call love beyond reason and understanding. It is beyond self-interest, but not connected to reason or understanding. But this is ordinary love. Anything that is not like this is not love. See also Maimonides, Laws of Repentance 10:1-2, where he defines serving out of love as doing what is true because it is true (and not for the sake of self-interest).