I never teach grammar rules. My students have had enough of that and after about 10 years they still don’t have their grammar straight.
However, I do correct incorrect grammar when I hear it. So does that indicate that I believe teaching grammar works? No, to the contrary. I have students that I have corrected for over a year on pronouns of gender and they still are frequently getting the pronouns of gender wrong.
So I will not tell you to take my word for it. Don’t take Krashen’s word for it. Don’t take Truscott’s word for it. Just do it. Do it yourself. Go ahead and correct your students. Make it Action Research. Do it and observe and after you observe then reflect and you will convince yourself. Choose a clearly observeable grammar point like pronouns of gender and correct your student everytime in everyway everywhere. Keep track of how many times your student gets it right and how many times he gets it wrong.
I suggest all teachers do this.