The question "does Linux contain
patgen" is meaningless. There is no Linux, there are many operating systems based on the Linux kernel, but which differ in many aspects from one another.
A GNU/Linux based distribution may even not have TeX, if its developing team decides not to include it.
If you have a Red Hat system, then the only way to know whether
patgen is available is to look for it in the directories containing executable programs.
TeX provided by your operating system
First, you may have gotten a TeX installation that was based on TeX Live but was packaged for your operating system. For instance, the free GNU/Linux distributions, and the distributions from Red Hat, Debian, Ubuntu, SUSE, etc., all make TeX installations derived from TeX Live available through their normal packaging system (
yum, etc.). If this is how you got your TeX, the timing and content of updates is entirely up to your operating system provider—contact them with any and all questions.
By the way, a native TL, which is typically installed under
/usr/local, and a TeX from your operating system can happily coexist, each with their own completely independent trees and programs. (Do not try to merge them!) So you could install a native TeX Live if your vendor is not keeping up.