Thank you for your answer. You pushed me in the right direction. I wasn't able to implement the method you pointed me to. It could have been that my RadScriptManager was located on the master page while my Upload control was on a User control nested in a page. Anyhow, this is what ended up working for me:
In this case my btnAttach is invisible and is only used to catch the postback on the click event.
__doPostBack('<%= btnAttach.UniqueID %>', '');