I would like to prohibit users who do not participate in certain projects from viewing them. Is this possible?
You can limit individual user views in Pipelines but not in Projects as far as I know.
In Pipelines, you can do it by changing the visibility setting on the top right to Only Owner (and followers). Then your project managers can add other coworkers to the project by adding them as a follower.
You can also set up group visibility settings to always make deals Only Owner and followers by default.