It will be an issue with the sticky sessions. As the DMS does all its work server side it needs proper session state management to work. You could do this on Azure using IaaS, but then you would be responsible for installing and maintaining the deployment of Sitecore on the OS rather than using the built in deployment features.
See this post by Jakob Leander for more info: http://www.sitecore.net/Community/Technical-Blogs/Jakob-Leander/Posts/2013/01/Why-we-love-Sitecore-on-Azure.aspx