Sounds quite do-able. I will first admit I don't know how postmaster works at all, so I could be way off in my suggestion. Regardless, you're looking at two plugins working together; a contact form & postmaster.
I would start with the contact form plugin, but modify it a bit so that it captures the users's information. Depending on your needs, I would either have a checkbox so the user could select which section they wanted notifications for, or have a hidden field that is pre-populated with the current section - then just pass that through.
If you want to have a visual representation of these records, you'll either want to look at creating entries for them, or just capture them within the plugin. I have an example of both to help get you rolling. DM me on the slack channel and I can send you my examples.
Here is where I'm not sure how to help. Once you have the information, somehow you'll need to tell postmaster where those records are, loop through and send an email. I'm guessing at this point creating entires that represent subscribers would be easier for postmaster to understand?