Benefits of Learning a Chinese Dialect in Addition to Standardized Mandarin
While I am not aware of any studies, I would add this:

From my own experience of trying to learn other dialects beyond Mandarin (Taiwanese, Cantonese), as well as simplified along with traditional characters, I'd tend to agree with the previous paradigm. 

The reason is that there is so much to learn in a single dialect that starting on another one would only get you to two "good" levels of a language, rather than one near-native level. I found that I was learning the same things in different dialects, but never really improving any one dialect beyond my current strongest (if that makes sense). 

So, unless you've already learned everything there is to know in your chosen dialect, or your preferences are to get to a certain level on mulitple dialects, I'd focus on one and make it awesome. Since you're a PhD student, I'm sure you can understand what I mean by "focus".

btw, interesting study that you posted.