Correct. After re-installing the package you just call library(pkg_name) and then test your modifications.
I am not sure what you mean exactly by compile. If you are referring to a new package version (ex: the latest version of devtools) this is not done on Github automatically. If a package is hosted only on Github, you typically download the latest commits when installing a package. If a package is also on CRAN, then the authors submit the new package version to CRAN.
Take a look at this section of R packages for some more information on different package states.