I do something similar except I make up a custom email every time. (No plus addressing at all, everything without a valid destination goes to the default account) It's rare something doesn't like it, most automated systems use the reply to header. Email lists are usually the ones least tolerant.
No, most companies that get the special email treatment don't accept email from customers anyway.
If I did it, I would have to set it manually. I don't know of an email client that supports setting the From header to the address in the To header of the relied-to message, but it feels like something that would be fairly easy to do as a Thunderbird plugin or whatever.