Yes. This aspect of the role is also partly where that title of Script Supervisor comes from.

As the Script Supervisor, you need to make sure that the script is actually shot.

Everything that is in the script needs to be actually filmed – each action, each line of dialogue. Yes, these change all the time while shooting. But any changes or omissions should be considered and deliberate decisions by the director – or at least she should be aware of them and give them her approval. What must not happen is that things are just missed in the frantic rush of trying to finish shooting a scene before you run out of time.

So, I keep track of what is actually being shot – how a scene is covered – and ensure that it actually is covered. I do this on my working version of the Marked-Up Script.