Anything is possible, I guess, but I feel like they're saving birds for a sequel down the line. I guess there's a possibility that we get a few species; some that are in WTEs and others that are in a new exhibit box type/size that's not walkthrough but... I think it's more likely that we don't get any flighted birds in PZ1 and they leverage the aviary system as a major addition in PZ2 down the line.
I'm all for birds, but I think it would be odd to add them this late in the game's lifecycle. Biodiversity would be pretty limited, it would introduce the possibility of bugs, etc.
EDIT: I also think there's an inherent difference in dinos versus birds. The pteranodon is pretty iconic. And for your average player, I'm sure that felt sufficient. With birds, though, I feel like if you were to introduce ~3 species it would just open the flood gates for people to want more because there's no way you can get proper biodiversity with a single DLC, let-alone a sub-set of species within a DLC that will also include mammals, reptiles, etc.