Is the hairdryer plugged into the wall?Wouldn't "the wall outlet" be correct?
(From http://www.usingenglish.com/forum/ask-teacher/155336-plug.html)
It's understood and doesn't need to be stated.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
As BobK said in another of your posts, sunsunmoon, "You can't expect everyone's use of language to be impeccable".