I think the trial should proceed anyway. If her background is relevant, so is his - he has a pattern of doing exactly the kinds of things she accused him of, relying on his position to get away with it. All that came out with this.
Her co-workers who found her directly after the incident would have something to say. So would those in the NYPD who routinely deal with these kind of crimes and were convinced credible charges should be filed against him.
In answer to your questions: yes; and of course lawyers do what they’re paid to do, and the more you pay them, the more they do.
The biggest problem is that the accuser will be forced to testify in a trial. If her character is so shady and her story has holes in it (I understand the latter to be the biggest reason why the case is likely to be dropped), then there’s no way any marginally competent prosecutor would let it go to trial. If he did, he would stand a very good chance of having the alleged victim turn into the star witness for the defense.