Re: Even if the charges are ultimately dropped by the Swedes
They would, yes. And by this point, the MET have spent enough millions of pounds guarding the embassy to make sure he doesn't leave that they can't really let him go. The term for skipping bail though is likely to be a lot shorter than a term for rape*. I imagine his biggest fear about that isn't going to prison: It's that once he is enjoying a stay at her majesty's pleasure, the US will decide to up their game, charge him with something (anything will do) and try to have him extradited directly. They can't really let him go unpunished because he would serve as an inspiration to others who might wish to compromise their security and embarass the country.
*I know it's a bit more complicated than that, but rape is accurate enough for these purposes.