Rich Text Fields are intended for formatting of text including links and images. Basically when you add proper HTML in there it should be sent on to your Published Page correctly, which would also be the case when editing it.
But please note that in the XPM (Experience Manager or UI-2012) view, you don't have a source view like is available in the CME. So it will be impossible to edit these HTML elements in XPM, as they are invisible in the browser.
Also note that ASP.NET Custom Controls are from a SDL Tridion perspective normal HTML elements, but your IIS application server reacts on their
runat="server" attribute and executes them (replacing the initial HTML element with something else).
Now XPM will see the changed HTML in your RTF field when editing, and will notice that it differs from the contents of the RTF field as it is saved in the CMS (I'm expecting it will notify you that by saying the preview is not up to date).