Is it required? No. It is recommended, however, to have the Global Catalog in the same site.
I would not recommend running with only one domain controller in your domain. Beyond just the fact that this is a single point of failure for your entire domain infrastructure, depending on how many users you have, you could also experience performance issues running on a single DC.
You can have a look at Microsoft's own recommendations on DC/GC placement with Exchange 2000/2003.
Because Exchange uses Active Directory, it is crucial that you
consider your Windows Server network topology as you plan your
Exchange deployment. In general, for best performance, you should make
sure you have at least one global catalog server in each Windows site
where Exchange is installed