It is secure to upgrade the RAM of a 32-bit Server? [duplicate]

I'm a new I.T. guy in my company, and while I was checking the servers, I found that, to my surprise, the server is using a 32-bit version of Ubuntu, but is using almost all of the installed 8GB of RAM.

I remember from my "Computer Architecture" classes that only 64-bit operating systems can use more than 4GB of RAM.

The question that follows is: Will it be able to use 16GB of RAM if I were to upgrade it?

(I can't test, because this is the core production server)

uname -a:

Linux bachue 3.8.0-19-generic #29-Ubuntu SMP Wed Apr 17 18:19:42 UTC 2013 i686 athlon i686 GNU/Linux

Output from top:

Simple. PAE.

From that link:

The Linux kernel includes full PAE mode support starting with version 2.3.23,[21] enabling access of up to 64 GB of memory on 32-bit machines. A PAE-enabled Linux kernel requires that the CPU also support PAE. The Linux kernel supports PAE as a build option and major distributions provide a PAE kernel either as the default or as an option.

So if it works fine with 8GB, it should work fine with 16GB.