I always RSVP. This one of my soap box issues.
I might call certain people to check on their receipt of the invitation, IF their attendance is critical and it's odd that they didn't respond. That's it. People who don't respond don't get planned for and should not show up expecting accommodations. They know this about me by now. I don't prepare a bunch of extra food; I plan for the expected attendees to have seconds, depending on the type of event. I let unexpected guests know that they need to wait until the people who RSVPed get their food and seats and they can have what's left over. I don't say it quite like that, but that's what it boils down to. I make a point of letting them know that I was not expecting them. Of course, this all depends on the event. If it's a simple backyard barbecue with an invitation to just come and enjoy, then I treat it differently.
I would be annoyed if you called after the deadline, but I would appreciate the effort. Depending on MY deadline for preparations, I might be able to accommodate you. I would let you know either way. I would not be bothered if you called to confirm receipt; I would probably feel ashamed that I had not done my part (which has happened). I would be super annoyed if you were planning to bring others with you and you didn't even RSVP for yourself.