My current department requires EMT-B for all firefighters. We're approximately 55% EMT-B and 45% paramedic.
We don't require paramedic certification to run on the primary rescue unit, but two of their captains are paramedics as are some of their other firefighters.
My previous department required that all of the rescue specialists had to be paramedics prior to applying for rescue training, but that department was about 85% paramedic with some EMT-I's and EMT-B's in the mix.
My F.D. requires EMT-B as a minimum, although most of our FF's are Paramedics. But to answer your question, no we're not required to be Paramedics to be assigned to the Heavy Rescue. Anytime the Heavy Rescue responds, there is either an ALS ambulance responding also or already on the scene.