It depends on the person. Some people may have only minimal impact. Others will have a fairly significant impact.
Everybody will have at least some negative impact on their running from lack of sleep.
It is hard to put a number on it though. The real impact will be on your training. One or two nights of poor sleep before a race won't be very significant on that race. Week after week of lost sleep will hurt your training quite a bit.
It isnt good for anything else in your life either. Lack of sleep if hurting your ability to learn, your emotional development, your social development, etc.
This school is doing you no favors if it is really assigning homework that is expected to take 4 hours a night.