Most likely I would use a repeater to do the same thing, unless I was planning on showing a very large number of rows.
You can do this with PHP. You would need to give your checkbox field a unique name. The you would need to create PHP that runs when the page is submitted to get your checkbox from $_POST and update the corresponding posts. Yes it is doaable. You can use an acf/save_post action.
As long as it’s not an ACF field and has a unique name it won’t be save anywhere by default.
