The short answer is no, we do not have auto-completion support for ASP.net tags. We haven't had a flood of feature requests for this, and I suspect that is because most folks doing ASP.net are relying heavily on the visual designer support found in Visual Studio.
After reading your post and taking a closer look at what it would take to implement it, ASP.net really is a pretty strange bird. You've got the <asp:yyy> tags, which look a lot like an XML tag with a namespace declaration. But of course the file isn't well formed XML by any stretch. And the declarations of the elements don't live in any sort of XSD schema, but rather the System.Web.UI.Control .NET namespace. So now we've got an HTML file, with some elements having valid declarations and context dictated with XML-schema-like rules, and said classes for those elements and their properties coming from a subset of the .NET framework. Oh, and it's "anything goes" inside the <ItemTemplate> tags...
Ok, please excuse the rant. I guess that's just the roundabout way of saying that there isn't any quick switch to flip to turn this feature on, and it's not a quick-turnaround feature.
However, there is something that can be done to give you a little help. If you examine the autocompletion file for HTML (the builtins\html.tagdoc file), you'll see that the declaration syntax for tags is pretty simple. It might be a lot of work as most of the ASP.net controls have a ton of attributes. But this simple sample shows you how you can add declarations of the tags.
private enum RUNAT_LOCATIONS{
server
}
tag "asp:content"{
attr ID;
attr ContentPlaceHolderID;
attr EnableViewState{
true false
}
attr RUNAT_LOCATIONS runat;
attr Visible{
true false
}
}
I would create this as a separate file named aspdotnet.tagdoc. Once you've added the declarations, go to Tools > Tag Files... , and highlight the child entry for the .vtg file under the "HTML" Tag Files entry in the tree. Then click the "Add Files..." button, change the file type filter to *.*, and locate your aspdotnet.tagdoc. After you've added your custom tagdoc, you'll need to click the "Rebuild Tag File" button to incorporate the new declarations. (Screen shot attached)