I'd check the registry rather than try to search the 100,000's of files on someones computer. On my machine, the key is Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Adobe\Acrobat Reader (this is W7 Ultimate 64bit). You'll probably have to find OS versions to figure out where it is for them.
For searching any PDF reader, I would rather check for extensions in registers. Here you would get also which application takes care of pdf files. By default Windows doesn't know this extension, so this can help to check whether there is or not any PDF reader.
For example check here:
(Windows 7/8 can have built-in PDF reader, have not checked it )