You will have to check with the vendors for specific compatibility questions as well as specific install and licensing ones. Generally many plug-ins will merely need to be copy&pasted into the respective folders, but some such as BorisFX or GenArts plug-ins may require version-specific installers.
The update from After Effects CC (12.0) to After Effects CC (12.1) doesn't change anything with regard to plug-ins and scripts. They should all just keep working as before.
When going from After Effects CS6 (11.0) to After Effects CC (12.x), there is a need to install into the new locations, but not a need to get new plug-ins in most cases.
See this page: