It's definitely possible. Windows Server 2003 R2 was a new release of the Windows Server 2003 OS, but, so long as you're licensed to use it, the actual installation is nothing more than an add-on to the base Windows Server 2003 OS (unlike W2K8 R2, which is a new release of the OS). Microsoft has documentation here and here that ought to be of help to you (the second link speaks to the specific details of upgrade from one type of product key to another and the restrictions therewith).
Basically, you're going to verify you're at the proper service pack level for whichever install procedure apples, then perform the "disc 2" setup (installing the R2 components). You're not going to have to reinstall the OS or rebuild the server. It's really fairly painless.