Currently there is a patch that once applied would take your version from ALM 12.00 to ALM 12.01 (there is also a complete installer that would install ALM 12.01 and requires the uninstalling of the currently installed version, which in your case would be ALM 12..00). If you go the patch route it is done and completed just as with any patch, the latter suggestion entails a complete uninstall of ALM 12.00 first, Either way, you would then have your projects in the latest version but if you uninstall/ reinstall you might have to remove (not delete) but remove the projects and re-add them back to get them running correctly.
Having said that if you are going through the process the current recommendation would be to uninstall ALM 12.00 and update to ALM 12.20 and then patch afterward. It seems as though ALM 12.01 is not getting recent patches as since it's release in June 2014 it hasn't been patched since. ALM 12.20 was officially released in November/December 2014 and has already received a new patch so the recommendation would be to go to ALM 12.20. You would uninstall the current version, install the new version, and then remove/re-add the projects, verify, repair, and upgrade them and all would be complete. The process is covered within the installation/ upgrade guide and assuming utilizing the same DB and app server, you should be able to complete the upgrade within a few hours and your verification would then take time, so dependent upon intricacy within a day should be easily obtainable, bar any issues or errors.
As for applying the patch to your current system, if a patch is released for ALM 12.01 due to the nature of the patching system on ALM12.00 (your current version), you would need to uninstall the patch applied and the 12.00 release and install ALM 12.01 GA release in order to further patch, which if going through this makes more sense to just skip the 12.01 release and proceed to the 12.20 release.
Either way you proceed, assuming you are using the same servers just make sure to not delete the repository files and the project DB schemas. It is always recommended to create back ups prior to performing any of these actions as a safety precaution and is just overall good operating practice.
I hope this helps,