Whilst a Singing Teacher can't turn you into Adele, they can teach you a lot about breathing techniques and singing from your gut and not your throat (sounds weird, but will make sense after a couple of lessens).
They can teach you about notes, and how to recognise, find, and hold them.
So yes. a teacher really can teach you how to sing. You may not be fantastic, or even stand out from the crowd, but you can be taught to be competent at it.
(My wife teaches singing from time to time).