Firstly, I'm not familiar with this passage, which secondly doesn't have to mean it's a fake - I read most of the journals in the edition by Frederick Pottle, who started to publish them mid 20th century, and only the German and Swiss travels in a scientific/academic edition as well. As you might recall, I noticed differencs, though not missing attempted rape scenes, more that where Boswell had transcribed his conversations with Rousseau in the original French (which btw is how we know most of his chats with Voltaire were in English), Pottle, aiming at a general audience, had translated them into English, same with the occasional German sentence, stuff like that. If it's an authentic passage, then my guess would be timeline wise it would belong in the London Journal era, because that was the first journal published, and it was when an in his early 20s Boswell still had daydreams of maybe becoming a military man (it's the posing as one which gives me that idea), and for a short while even had a highway man fantasy after watching The Beggar's Opera and being impressed by Macheath - and since Pottle had no idea how positive the journals would received, he might have excluded this. Otoh: Mid 20th century was sadly pretty blind to attempted rapes, and the whole selling point of publishing Boswell's London journal was "here is a warts and all real life Georgian journal, and by Johnson's biographer, no less", and the published London Journal includes bits like him being impotent the first time his current crush Louisa says yes to sex (lots of woe, what must she think of me!), then a later description of their second attempt where glorious sex is achieved, and then later grrr, argh passages when he realises he's caught the clap and since she was the only woman he's been with the last three months it must be from her.

Did he see the error of his ways: one reason why I wouldn't have thought Boswell would be the type to force himself on someone is that he reports in his journals not just successful sexual (and/or for that matter romantic) encounters but also unsuccessful ones, be it due to an attack of impotence or because the woman in question turns him down. Or sometimes he doesn't have enough money with him - I seem to recall a later entry featuring a prostitute where it's a hand job only because of the money factor. And in none of those cases (that I recall) does he use force. Also, he comes across as being into enthusiastic consensual particpation, as in this passage in the London journal:

Indeed, in my mind, there cannot be higher felicity on earth enjoyed by man than the participation of genuine reciprocal amorous affection with an amiable woman. (…) I am therefore walking about with a healthful stout body and a cheerful mind, in search of a woman worthy of my love, and who thinks me worthy of hers.

Then again, here he's not speaking of a quickie with a prostitute but a romantic (and sexual) longer affair, and it may just be that he's dehumanising prostitutes in his mind enough to think they have no right so say no once they've said yes, as opposed to women of his own class (or slightly lower). But, like I said - I don't recall other examples of him attempting force on a prostitute (and there were a lot of prostitutes). He does have enough insecurities about status to make this whole being satisfied about being recognized as a gentleman sound believeable; when he's studying law in the Netherlands, he falls in love with a Dutch lady who is both his social superior and better educated and smarter than he is, which is a problem for him, though the relationship with Zelide (not her real name, but his journal nickname for her) goes on for quite a while and he keeps corresponding with her after leaving the Netherlands, and let's not forget that when travelling through the German principalities, he promotes himself to Baron von Boswell because the nobility still rules all in said principalities. And then there's the whole hang-up about being Scottish at a time when Scots are booed and hissed at in England, but that comes without any sexual connotations.

In terms of using social force in non sexual situations, that's actually one of the things that makes me like Boswell, because he doesn't even where it would be typical for the day that he does. For example when his little daughter says "I don't believe in God". I mean, he's horrified. But he doesn't react authoritarian by ordering her to stop saying that, or punishes her for saying it in the first place. He first tries to find advice in the 18th century equivalent of parenting guide books, and when he doesn't find any, he simply asks her why she said that. (It turns out she's heard beloved relation X is with God, which made her think God kidnaps people and kills them, and if she doesn't believe in God this won't happen to her. Boswell and Mrs. Boswell gently tell little Veronica this isn't how it works and explain instead of bringing down the parental hammer a la FW.) And a lot of the clients he takes as a lawyer are down on their luck poor folk like John Reid who is a repeat offender in sheep stealing (Boswell manages to get him off the first time, but the second he doesn't manage it; what he does, though is be with him till the end, share some whiskey, and promise to help the widow and the kids as much as he can), or indeed a female convict from Botany Bay who has made it back to England and would rather not be send back to Australia or killed. So here you have him siding with the powerless without much benefit to himself, not even in terms of prestige (no one ever heard of John Reid, Scottish sheep stealer with a big family, before Boswell's journals were published centuries later). (Boswell seeking the company of the famous certainly isn't just about curiosity but also about status, is what I'm saying. Boswell helping out the poor, otoh, is not.)

In conclusion: I can see why Damrosch was appalled - it's an appalling scene. And adds to the contradictions of Boswell, clearly. Whether it defines the man is up to the individual beholder, I'd say.