Yes, "HTTPS Everywhere" includes your dumb server. That's what everywhere means.
It’s hard to pretend that privacy isn’t important these days when every other day there’s another story about a data breach leaking millions of peoples’ private data into the public when they were really meant to be shipped off to a government surveillance program, or that Facebook was again lying and selling your account security phone number to every company who had spare change to spend on it, or some other equally dystopian nightmare. Unfortunately there’s not a lot any individual person can do to prevent that sort of stuff (except maybe deleting your Facebook, which you should definitely do), but you can limit what you do out in the open by encrypting everything.