Typically yes! The third person character usually uses generic animations that seem like they would fit the animations of the first person character. But typically while in first person mode, your third person animations wont matter as your first person character’s animations are what determine the location of your bullet projectiles/traces. Then the third person character uses its generic animations to simulate the same effect to other players. But you will still want to use animations that allow for your character to shoot properly in tps mode.
Also, there are some situations (non-traditional cases) where game developers will use F/TPS characters. All this means is that they use 1 mesh for first and third person and they have specific animations that align the FPS camera and the TPS camera in accordance with realistic alignment. This method is the newer style of TPS/FPS style games and requires a decent knowledge of animation offsets and algorithms that allow for proper animation alignment in accordance with the respective camera. You can learn how to do this style character in UE4 pretty easily if you follow enough tutorials. Goodluck!