Yes...
The downloaded system installer is in your Applications folder.
Save it to an external drive before you start the install.
If you have already run the installer to upgrade your system, then the installer deletes itself as part of the install, so only the copy that you save before installing will be available for you to use in the future.
If you want to save it, but forgot before running the installer, you will need to download it again, just to save it.