Reading by itself doesn't.
But listening and , well, speaking does :-D
Speaking in its core is auditory and Reading is visual.

In a similar way you could ask if training your sprinting abilities makes you a good marathon runner?
Both are ways of running (like Speaking and Reading are ways of communicating) but the chemical processes in your body are not the same (like the way your brain processes auditory information is different from how it procsesses visual information).

If you wanna improve an auditory skill set you have to train auditory. You can do that by training your capabilities to hear the target language correctly and train your capability to mimic the sound correctly.

greetings
Tobi

Reading helps you learn new words in context and see grammar "in action", and since speaking requires vocabulary, I would say that reading can improve your speaking in that sense. But of course, as the others have said, speaking requires more skills than just words, such as pronunciation and actual speaking practise, which you don't get reading newspapers.

I kind of agree with James in that reading books might actually be more helpful than reading newspapers. Fiction books (with dialog) give you more "real world" examples of the spoken language; newspapers are often written in a style which is slightly more formal and different from how people speak.