You'll be able to speak English just by listening to it.
If you just listen to this material, you'll become a good speaker of English.
Just listening to this material will improve your English capabilities.
聞くだけで、は、just by listening to it (material)とするのがよいと思います。
英語が話せるようになる、は、
will be able to speak English
will become a good speaker of English
will improve English abilities
と様々な言い方があります。
日本 
