No desires?  I think I'd find it perfectly possible to watch the episode and make a case for asexual Sherlock - what we're seeing doesn't have to be sexual desire.   They really do seem to have covered all bases .
 

http://www.benedictcumberbatch.co.uk/benedict-cumberbatch-and-louise-brealey-discuss-sherlock-at-cheltenham-literary-festival/

And as for Irene Adler?  Well, you say he was beaten by her, but do you know what they got up to in Islamabad? Because I do.  There was no beating. It was all very loving.

So according to Benedict, no beating and no begging for mercy.   But he does say in the same interview that he makes up backstory. 

Also, this was part of a response to a question about the portrayal of women in Sherlock: "Do you find there is anything problematic with how woman are written on Sherlock. Molly as the unrequited love, Mrs Hudson as the archetype mother and Irene Adler as the only person who bested Sherlock, fell in love with him and was beaten by Sherlock."  So Benedict's response may be more about defending the portrayal of women, than about his view of the relationship between the characters.  I haven't heard the audio of this part (has anyone, or was anyone there?).  This might have been a jokey answer.  In the transcript he seems to mishear; the audience member's concern is that Irene is shown as being beaten by Sherlock (rather than beating him, as she did in the book).

Loving, rather than passionate and exotic?  I suppose I can buy it (even if I'd be a little disappointed).  There is Irene's suggestion of "dinner", which has no kinky connotations ... but that's about the only suggestion that doesn't have kinky connotations.   She does have two personas with Sherlock (hair up, hair down, to be brief ), and both seem to intrigue him. I still think there's lots of ambiguity there, and will continue to see what I want to see . 

I think that whatever she says about her sexuality, she's attracted to him.   That's how he wins the game, isn't it?  She shows signs of arousal when she's in a sexually charged situation with him (talking to him about sex).   Whatever Sherlock feels for her, I don't think there's any doubt that she desires him.  I think even the code showed that.  It's not something clever, it's not about finding him interesting.  It's all about falling for him. 

Personally, I think it's a two-way attraction.  Sherlock looks so hurt when he exposes her that it seems to me that he's repressing exactly the same feelings for her.   That's partly why he knows.   They know what each other like.  (That's the point when he guesses the code, when Irene says Moriarty is her kind of man ... and Sherlock knows that he's her kind of man).  They reflect each other in various ways (clothes, hair, etc.).

I did say that the sub is in control in a business arrangement (like Irene and her clients).  But I think that in a personal situation in a relationship, it's different.   It's mutual.  Sherlock and Irene have learned to read each other, and that's the really important thing. I think they'd do OK, were they to indulge  

There's the little scene where Irene "beats" Sherlock to get the phone back.  She's reluctant to hit him outside a sexual situation - she seems frustrated that he won't give the phone back and that she has to do it.  Running the riding crop over his face was a bit cheeky and self-indulgent, I admit, but it wasn't something that was actually causing him pain or harming him.  I don't think she'd be an abusive top.