They'd still have shields, moore, hellickson, archer, cobb, and niemann. That would be a very solid top 3 with some good depth to round it out. There's no reason they would'nt be able to compete with that rotation.
Shields may be gone this offseason. Moore, Hellickson are, at best, 2s. Everyone else is a 3 or worse. They need Price in order compete. He's the best pitcher on your team unless you're the Tigers or, maybe, the Mariners.
Any deal for Price will include Rendon.