Thanks for all your helpful responses. Just thought I would add Go Daddy's response for completeness.
I also posted a follow up question: How to run a .NET Class Library on a Go Daddy server?.
Thank you for contacting Online
Support. It is not currently possible
to run .exe files on our shared
servers. You would need to be on a
Virtual Dedicated or Dedicated Server
for this type of support. You can run
.NET code from a class library as long
as it runs within Medium Trust.
Trust level refers to permissions set
in the Web.config file that dictate
what operations can and cannot be
performed by Web applications. Our
ASP.NET 3.5 shared hosting servers use
the default Medium trust level with
the addition of OleDbPermission,
OdbcPermission, and a less-restrictive
WebPermission.
Applications operating under a Medium
trust level have no registry access,
no access to the Windows event log,
and cannot use ReflectionPermission
(but can use Reflection). Such
applications can communicate only with
a defined range of network addresses
and file system access is limited to
the application’s virtual directory
hierarchy.
Using a Medium trust level prevents
applications from accessing shared
system resources and eliminates the
potential for application
interference. Adding OleDbPermission
and OdbcPermission allows applications
to use those data providers to access
databases. WebPermission is modified
to allow outbound http and https
traffic.
Please let us know if there is
anything else we can assist you with.
Sincerely,
Graham P. Online Support Technician