As long as you are following good maintenance practices, then no, the only added risk of damage comes from the instrument not being in a protective case. (Hopefully the instrument isn't sitting on a stand long enough for it to collect dust.)
Of course, on a clarinet, part of good maintenance practice is swabbing out the moisture after every playing session, and many clarinetists do this separately for each joint so they don't miss any moisture collecting near the corks. Leaving a reed on the mouthpiece for extended periods of time will get you a moldy mouthpiece. But as long as you are properly caring for the instrument and not putting it in harm's way, then leaving it assembled should be fine.
The reason most teaching resources recommend that one puts away their instrument back into the case is that it's far too easy to not follow good maintenance practices. The simple act of, say, taking your mouthpiece out of your trumpet after you play helps to ensures that the mouthpiece isn't going to get stuck in.
Similarly, if you do decide to leave your clarinet out of the case for extended periods of time, every few days you should give it a quick once-over to polish any dust off and make sure all of the corks/joints move satisfactorily.