If a person has the mean look status and they baton pass, will the person that is in battle after the switch still have the mean look effect?
Mean Look prevents the target from switching out or fleeing (including via Teleport). The effect only applies as long as the Pokémon that used it remains in battle.
The affected Pokémon can still switch out via Baton Pass, but in that case, the Pokémon that switches in will now be affected. Affected Pokémon can also switch out with U-turn. Conversely, the Pokémon that used Mean Look can switch out with Baton Pass and the effects of Mean Look will still apply. Also, if the affected Pokémon is Roared at or hit with a Whirlwind, they will still be switched out.
If a wild Pokémon uses Mean Look on the player's Pokémon, the player will be unable to escape, unless the player's Pokémon has Run Away or is holding a Smoke Ball.
So yeah it would source: Bulbapedia