How much of a role does achilles tendon play in plantar fasciitis?

It can: A tight tendo achilles can limit ankle motion. If so, that can increase pronation in the foot, causing strain in the arch and contribute to plantar fasciitis.

Calf contracture: The calf, not the achilles is the entire problem and has everything to do with plantar fasciitis.

Large roll: I always check the achilles stretch on people with foot pain, especially heel or arch pain. It is usually helpful to stretch the achilles with plantar fasciitis.