It should be doable, but probably with a few caveats. First, you can't use standards mode. You'll have to use quirks mode. Microsoft still hasn't fixed HTML Applications and their dialog windows using standards mode. And I wish I had documented all of the research I did on this, but I didn't, so I'm going to venture a guess that you should be designing for IE7. That doesn't mean features (or fixes) of IE8, IE9, or IE10 won't work, but you'll just have to try and see.
I'm sure there will be other gotchas. If you need some help getting something to work, I'm happy to take a look. Post here or email me directly (support@thetournamentdirector.net). Included with the software is the "Minimalist" layout, which is done as an HTML layout. In coding up that one I ran into an IE bug that I had to actually change code in the TD to work around. I understand how frustrating it can be.