Yes of course!
Make sure you are an administrator level so you can do anything!
Firstly give your comms people have the appropriate user level Dashboard>Users (Safest is subscriber if no posting privileges, or higher if they can do blog posts etc).
Next make sure website user accounts are tied to directory entries (by editing individually or Church Admin>People>Create Users)
Then head to Church Admin>Settings>Permissions
Add names to all the tasks and hit save – they will only have access in the plugin backend to what you have given them permission to do.