Briar personally doesn't want people and Pokémon being separated because she sees them as useful. She doesn't think humanity would last without Pokémon helping, and humans also help Pokémon thrive in their environments, specially when it comes to human-made species. So yeah, they could possibly live without humans but wouldn't last as long because it's a symbiotic relationship.

... And also she's kind of fond of Pokémon so she can't imagine a life without her Pokémon.