Is this allowed? If not, can this be accomplished inherently by overloading the implicit/explicit conversion operators?
Is overloading the "is" and "as" operators allowed?
No.
If not, can this be accomplished inherently by overloading the implicit/explicit conversion operators?
No. The "as" and "is" operators tell you what a thing really is. They pay no attention to user-defined conversions.
See
http://blogs.msdn.com/b/ericlippert/archive/2010/09/16/is-is-as-or-is-as-is.aspx
for some more thoughts on the "as" and "is" operators.