Got it working. Here's what happened.
The q2admin download that I had found from q2admin.net came from the following link:
http://www.q2admin.net/index.php?i=f.
This is labeled simply as "server install" on the main page without mentioning action quake2. However the mod is also irrelevant.
Inside this zip the file structure exists as such. Q2server containing the folders baseq2, release, action, and q2admin. When you extract this file to c:\quake2 it creates the folder c:\quake2\q2server and then the respective directory structures c:\quake2\q2server\baseq2, c:\quake2\q2server\release, c:\quake2\q2server\action, and c:\quake2\q2server\q2admin. Simply put this file was incorrectly zipped with the wrong file structure.
The "correct" q2admin downloads found at
http://www.q2admin.net/index.php?i=d include only the gamex86.dll and do not include the installation information or configure files. The installation information also warns that you need these configure files to run quake 2 admin. So downloading the action q2 "server install" file ad discussed furst is a better choice to have a basic setup for q2admin to work off of.
However, The installation information inside this "server install" zip does not address specifically where these configure files need to be. The correct answer is to extract the files into a temporary folder. Rename the root "q2server" directory to quake2 and zip the files into a new zip file. Then you can extract them to c:\ and the file structure will be restored to c:\quake2\ with the respective structures of c:\quake2\baseq2, c:\quake2\release, c:\quake2\action, and c:\quake2\q2admin. (This also depends on where you have quake 2 installed to. For example I have it isntalled on d:\quake2 and then extracted my new zip to d:\)
Q2admin is not properly installed until you see the q2admin version number printed immediatly above the "init game" text in the console after you start a game. In 2 instances involving several re-installations of q2admin, the c:\quake2\release folder is never accessed by a standard version of quake 2, either in dedicated or normal loads of the game. It seems as though r1q2 must be installed, and you must be using the r1q2.exe entry point in order for this c:\quake2\release folder to ever be read.
Simply put (and correctly predicted in the original post) stanard quake 2 does not seem to read from c:\quake2\release and c:\q2server\release and c:\quake2\q2server\release are the incorrect paths for the q2admin gamex86.dll.
To be exact to correctly use q2admin the following files must be in the following places:
R1q2 must be installed
Put the q2admin dll into c:\quake2\release\gamex86.dll
Place all q2admin configuration files into c:\quake2