Not exactly. It depends on how a trainer meets their potential trainers. In fact, I heard that some trainers are willing to let them go if they are uncomfortable with letting go their habitats. Of course, there are some trainers who are willing to capture them against their will.

As for me, I just met Garchomp when she was on a rampage as a Gible. She managed to calm down after I comforted her and ever since she didn't leave by my side. You could say everything she did was her own will out of our friendship.

But regarding them as pets, they can choose not to capture them for their sake. But that would leave them as wild Pokemon and has a higher risk of being captured by someone else.