If you do not have a Lync client on your other side, you will have a hard time getting application sharing to work. Using an RDP client will not work, since RDP is just a connection to a machine rather than a SIP call. The underlying protocol for the app sharing stream might be the same (I dont know about this), but you'll be missing the parts that deal with the whole Lync connection.
Michael Greenlee has written a bit on the subject of Application Sharing (which is used to share desktops) here: Handling application sharing calls in UCMA, and an MSDN thread on the subject is here: How to handle Application Sharing Invitation, maybe this helps you?