No, health is a statistic that adjusts the speed of your driver. Depending on your driver's stamina, which is trained through physical, is how much their health and therefore speed drops across the race. However, after the race it resets to what it was before the race -1. 100% is the max and 1% is the min. You ideally want to train the doctor every race to keep their health and moral at what they were before a race, and phyiscal training of course improves health. You can also spend 100 RP on fully revitalising a driver of your choice which you own.