I reckon that they'd give you a preference, yes. Although it depends on the number of en-suites they have, I suppose.
I think unis are generally very understanding about that sort of thing. When filling in some accomodation forms for one of my unis, they asked if there were any medical reasons as to why I couldn't have a shared room. I emailed the admissions people, to tell them that I had very bad allergies which led to extremely bad snoring, and did they think this qualified as a reason, and that I was happy to get a doctors' note to prove this. They sent me back a very nice email to say that yes, they would consider this a genuine reason, no doctors note needed (suprised me a lot!) and that I wouldn't have a shared room. This struck me as very friendly and helpful of them, especially as it was my insurance choice, and so I would have been more likely to get a shared room.
I know its a bit of a wussy reason, but I think I'd end up murdered by any poor sod who had the misfortune to share a room with me. XD