Does IELTS (TEF) influence your CRS score. Yes heavily and more than anything else. Language tests results can influence up to 56% of your points, which is more than education, your age, or your work experience.
The theory behind is that as people are more aware of the points distribution, they are trying to improve language test score more than anything else (you can prepare at home and the test is cheaper than 1 year of MBA, and unlike PNP, this option is opened to everybody).
And when there are more people with higher CRS competing for the same amount of ITA that will in terms influence the ITA and the draw score as well.