Hey Justin,
You can absolutely make it with this engine but your gonna have to work from scratch to get what you want exactly and for that kind of game. You should focus on learning everything about Sprites and UMG in unreal for that kind of game.
As far as the environment goes, fix the camera angle on the third person template to emulate the pokemon 45 degree look. Then its a matter of adjusting your 3rd person character components to display sprites instead of 3d skeletal meshes and disable the jump.
The levels can be horizontal placed sprites with player block collision so you can walk around the picture.
Parts that you dont want the player to walk on set blocking volumes.
Random encounters can be built using trigger volumes that randomly generate numbers as you walk on it with each number assigned a different call event that specifies ‘the pokemon that appears’. As an example numbers that get generated 1-50 do nothing 51-60 is one type 61-90 is another type 91-98 is a more rarer type and 99 is the rarest type.
Other trainers would be the same thing, player enters a trigger volume player controls are negated, the walk up anim plays, and then you do the socially acceptable dog fight thing.
No joke I can probably prototype this in a few hours with basic assets.