Can we say that the Turing test aims to develop machines or methods to reach human-level performance in all cognitive tasks and that machine learning is one of these methods that can pass the Turing test?
The Turing Test is essentially a benchmark or challenge problem. It is a task that AI researchers would like to be able to solve.
Machine learning is a technique. It is a tool developed by AI researchers to solve various problems. Some kinds of machine learning are applicable to the Turing Test, but others are not. Machine learning is also applicable to a wide range of other problems.
Jobst Landgrebe and Barry Smith, in the paper Making AI meaningful again (2019), argue that machine learning is not sufficient to build an AI that is able to fully (like humans) understand language. They state that current machine learning (or stochastic) approaches might not take into account a lot of contexts while understanding language (e.g. at machine translation), because of the eventual lack of associated data or because of the big number of possible solutions to a language understanding problem.
If understanding language is a necessary skill to pass the Turing test, then current machine learning is not sufficient to build an AI that will pass the Turing test (according to them).