Is there a way to install a racket package either:
There are two questions here. The first one being if it's possible to create a racket package as a statically linked native executable. If you mean a single executable with all the libraries statically linked, the answer is no. You can, however, create a racket distribution of your application that you can then install on machines without racket. See https://docs.racket-lang.org/raco/exe-dist.html
The second question is if you can use raco install to install the above mentioned package and the answer is no. raco will install pkgs, libraries into the system, for use with racket but not an application in a system-wide manner.
My advice is to use raco distribute
and then use a system installer get it into the target system. For arch linux, I would create a raco distribute
of my application and then I would create an AUR to distribute my application to my target users.