I'm assuming it will open with fastpass, but then it will get to a point where it doesn't need it (a la Philharmagic). It's comparable to Haunted Mansion, which is an extremely popular ride with fairly reasonable wait times, because omnimovers are quick loaders. (And if Mermaid doesn't have a line stacking system, like the stretch room, it will load even faster, like Nemo.) We all know it'll be hugely popular at first because it will be brand new, but I think as everyone gets used to it and it becomes older, lines will go down and fastpass will merely bog up the system like it did at Mansion (which never needed fastpass to begin with).
I'm not sure if Mermaid and Dwarfs having fastpass will impact something like Space Mountain. A lot of people who will get FPs for Mermaid and the mine train will be getting them because their child is too little to ride Space, so even if Mermaid and Dwarfs didn't exist, those guests wouldn't be getting Space fastpasses to begin with. Although I can see it having an impact on things like maybe Buzz Lightyear or Winnie the Pooh. Things that young kids can go on. Having more 'little kid' fastpass attractions will ease the fastpass load on those types of rides.