I reckon that people who want to learn a certain dialect ,they only need that for a certain purpose and not for exploring the whole Arabic culture. Overall, peole have the right to choose what they want to learn. For myself I always recommend people to learn Fusha, because when you learn Fusha, it would be easy for you to talk with all Arabic people regardless of their dialect and sure they will respond to you in Fusha because they all know how to speak Fusha unless they are not Arabs.
For non native Arabic speakers, learning both MSA and a certain Arabic dialect at the same time, it's something almost like learning two different languages. Overall ,I don't recommend you to do so unless you have to do it. When you finish learning MSA , you may try to learn a certain Arabic dialect.