Is it possible to reuse a website project?

If there is a fresh installation of WordPress and WPML, this is not supported.

On the other hand, if WPML’s database was not changed while creating the new website, the association is preserved. There is no way to change the website project to which WPML connects, a new project is created for every new WPML install.

In case it is necessary to have a production and staging website, WPML database should be copied from one to the other. Then, they will be associated to the same project.

If the translation pickup mode is set to automatic, only the original site will be able to receive the translated content. Therefore, if you have two websites pointing to the same project, it is best to set the pickup mode to manual. Then, both websites will poll ICanLocalize to retrieve the translations.
In order to change the translation pickup mode, go to Multilingual Content Setup and look for the “Translation pickup mode” box:

Reusing a website project