They will help. But taking IELTS classes is not the main factor in getting a better IELTS score. The main factor is your actual level of proficiency in English.
Many students stop taking General English classes because they say that they need to focus on IELTS. This is a good idea if you plan to take a test in a month. IELTS classes will help you avoid getting a lower score than you deserve, they won't help you improve your score.
If your English proficiency is basically a 5.5, then taking IELTS classes will make sure that you don't get a 5.0. But it won't help you get to a 6.5. It might help you get to a 6.0. But purely focusing on the scoring criteria, essay templates and cohesive devices is not going to make a very big difference. So, taking an IELTS course for more than 10 weeks instead of a more advanced General English class. Certainly for students in Elementary to Upper Intermediate it is more useful to spend more all of your time trying to work on your General English than to look at IELTS. Many students believe that what they test in IELTS is information that can only be found in an IELTS class, actually it is all English.