Is there some way I can use the Software Installation GPO in Server 2012 to deploy things like Java and Adobe Reader? Problem is these are .exe setup files and it seems that Software Installation GPO requires a .msi file.
I have read about .zap files but Server 2012 does not seem to support these, .msi files only.
You'll need an .MSI to deploy through GPO. There are ways to convert your .exe to .msi, or wrap your .exe in an .msi, but both products you mention have .msi packages available.
Java:
How do I deploy Java using Active Directory across a network?
Adobe Reader:
Distribute free Adobe Reader in volume
For the Adobe Reader, you'll need to fill out an "application" to receive a link to the downloadable .msi.
If .msi packages weren't available, you could use something like PsExec to deploy the .exe.