The short answer is always 'yes', you can.

IP version 4 resources (that's the IP addresses we currently, mostly, use today) are limited.

We don't want you using addresses where you just don't need to.  We especially don't want you doing it just because we're to lazy to help you not use resources you don't need to.  For example, if you have an application that needs to talk to seperate database servers in the same rack, those db servers don't need individual public addresses.  We can set up a private network for you so your application and support staff can do what they need to do.