Is there a way to create a hotel roommate system for a conference?
There is no off-the-shelf module to do this, but you could set something up with a custom Room share request content type and then Rules and Entity Reference to handle the scheduling and assignments.  Combining Rules, fields (via content types), and entity references should be flexible enough to handle such a workflow but it will require a little work to set up and may be too much work in your case.

Unless this is a huge conference, you might just go with the built-in forum module and allow users to post to the forum if interested and sort things out themselves.  It requires very little set up and that way if your users don't actually use/need the feature then you won't waste time developing it.