Is there any proof that learning ones own dialect will improve ability in Mandarin?
Even the statement that learning ones own dialect improves ability in Mandarin may be true, it doesn't necessarily apply to those who study Chinese as a second language. 

If you're looking for ways to make learning Mandarin easier, my personal opinion is: don't torture yourself. I speak Shanghainese (a kind of Wu dialect) as my native dialect. While I am talking (in this dialect), my work mate who comes from Northern China doesn't understand what I am talking about at all. You can see the huge distinction between Chinese dialects!