<p>Are there any issues with running an asp.net 1.1 application under windows server 2008 64-bit web edition?</p>

I have never tried it myself, but I did find the following pages that you might find interesting:
This blog
has an in depth walk through of configuring ASP.NET 1.1 on Windows Server 2008. The author does not say if it is x86 or x64, so I would just assume its x86. But either way, it looks like the author had to jump through some hoops to get the ISAPI filter setup correctly.
I also found
this thread
on the IIS7 forums where someone discuses having poor performance from ASP.NET 1.1. on x64 Win2k8. So from poor performance I would assume it worked to some extent. Unfortunately towards the end of the thread the author mentions encounter 500 errors, and then the discuss stops :-(
So from what I've read I would guess that its possible, but I would also guess that you would have less hassle if you could find some alternative that didn't involve both II7 and x64.