No, you cannot befriend or recruit Rotom in PokéPark Wii: Pikachu's Adventure. Rotom appears as a special story character but is not obtainable as a playable partner.
Rotom serves a specific narrative function in the game's story mode. You'll interact with it during certain events, but it doesn't join your team like other Pokémon you befriend through attractions.
If you want Rotom as a companion, these titles offer that opportunity. In PokéPark Wii, enjoy Rotom's story role instead!