She does, but she should have given him the choco regardless even with the rest of the so-called 'harem' (looking more like just a friend group her tbh) being around. She's the legendary Void Hunter, none of them would get in her way except maybe Burnice and that not out of malice.
If Red doesn't want to be found, I'm not sure even the Old Man can find her.
To be perfectly blunt with you - I wouldn't be surprised at all if everything Kal trained Red to do was based on what Grandpa and the original Doctor could do. Red's a damned good hunter and assassin, but she's probably not on either of their levels yet.
