No. Heart rate range and VO2 max are 2 separate variables. Interestingly Paula's speed at a given heart rate improved significantly - at 180 bpm her running speed improved from 14 to 19 km/h.
As long as hearts are not diseased they do not limit our running - they pump out what the veins return to them. The rate limiting process is what our mitochondria can do. Similarly, our lungs do not limit us as long as they are not diseased.