You don't need redirect to get at the cookies. All you need is a delayed load content.
Basically, I believe the following would work:
The 'GET /index.html' response sets the Cookies (they come in the header, and are stored before index.html is received and rendered).
You can than check for cookies while serving say 'GET /TinyImage.gif' if you don't run into caching problems and respond to images dynamically.
So, the final problem, is how do you inform the user about your findings from the TinyImage request? Definitely not easily, but if you use IFrame instead of a simple tag, you can essentially have two GET requests for a single page render.
Or, you can be really, really insane and actually stall the first GET until the second GET confirms the browser settings. This is for some HTTP wizards, but if you can wrap your head around Comet (not AJAX, Comet!), it can come in handy.
It's definitely possible, just tricky. Would I try doing so in ASP.NET? Can't promise anything but it will be a neat thing to share.