Yes, this is possible with Airtable. I’ve actually done this very thing and scaled it across a large organization. There are several variables to consider here like the complexity of the project template and any variability across projects. There will be many more variables to consider as well. The most significant effort you will have is creating the template, as you want to make sure you work through any implementation challenges from the beginning.
For a short description of the approach I took, I created a project template that I could duplicate for each project. Then, I created a global base that all projects sync to. This gave me a project-by-project view, allowed for each project team to have their own space, and allowed for the global view.
If you would like more detail, I’m happy to work with you on getting yours set up and running so you don’t have to work through the same challenges I faced.