Frankly, I don't think that sexual expeience would do much to help resolve Shinji's issues. (although it might help Asuka and perhaps Rei.) Shinji's problems go deeper than his sexual frustration, and he's unlikely to break out of becoming an entirely passive character just from losing his virginity. Keep in mind that Asuka's flaw is that she's too insecure in the way she interacts with people and Rei's flaw is that she doesn't interact with people. Meanwhile, Shinji's problem is that he refuses to interact meaningfully with others, never making an effort to get what he wants and complaining when he doesn't get it.
The reason for this is the death of his mother and the emotional distance of his father, which led him to conclude that the best way to do things was to give everyone else what they want, since his desires aren't important. Asuka, in losing her mother, concluded that she had to be the best at everything to have any value, otherwise she would be abandoned and rejected. Meanwhile, Rei, through dying for the first time, began to believe that she had no desires.
In other words, Rei needs a hug, Asuka needs to be told to chill out, and Shinji needs a slap in the face.
Shinji's head isn't too hard to get into though. Not nearly as hard as Gendo's anyway. :)