The answer is yes, of course it can be taught, it's just that the way many textbooks tell us to teach it is actually one of the least effective. Most textbooks will have you drill pronunciation with repetition of the vocabulary.

Should pronunciation be taught?

Pronunciation teaching should almost certainly be included in other types of lesson, but in many cases separate lessons may be useful as well.

Does pronunciation need to be deliberately taught?

Since pronunciation is part of speaking, it is also physical. To pronounce a new language, we need to re-train the muscles we use to speak. And pronunciation involves listening to how the language sounds. We can practise by focusing on connected speech while playing fragments from speech recordings.