Is it a good idea to attach a pergola to the roof?

I'm looking to extend my outdoor patio area. The rear of my house has two different roof line heights. The higher one, which is coming off the main part of the house, I want to install an insulated aluminum patio cover. The lower one, which is coming off of a bedroom, I want to attach a pergola to the roof. This location is also where I'm wanting to put a small outdoor kitchen (i.e., built-in grill, small frig, bar overhang countertop, storage space). I'm wanting to go with a pergola for the lower roof line primarily so that the smoke coming off of the grill can easily exhaust in the open air. However, from my research so far I've been reading from some sites that his might not be a good idea to tie a pergola into the roof. So, is it or isn't it a good idea?