It does actually have an impact on your charging rate IF you're getting more than 108 kW when the second car plugs in. If you've plugged in relatively recently and had a low enough SOC so that you are getting over 108 kW, your charging rate will drop to ~108. This happens due to the way that traditional superchargers dynamically switch power. The superchargers are made of 12 AC to DC chargers (rectifiers) just like what you have in the car for charging at home. Each is capable of the same ~12kW. So, when all are working there's ~144 kW available. But, in order to be balanced on the 3 phase AC power that's being drawn from the grid, the architecture of the superchargers bundles them in groups of 3. In effect, the 12 are really more like 4 groups of 3 each. Any car plugging in is guaranteed the power from 1 group of 3, which is why the second car to plug in will only get around 36 kW if the first car has a high charge rate. But since the new car is getting 1 group that only leaves 3 groups (9 chargers) for the first car, hence the limit of ~108 kW. If the first car's charging rate has already dropped below that point then they won't be affected, but if they're still above it then their charging rate will drop to there. Subsequent group shift--giving access to additional power in blocks of 36 kW--will happen once the first car's rate drops below 72 kW, then 36 kW.
The above is assuming that the supercharger is in perfect working order. However, if one or more of the individual chargers within the supercharger is faulty, you could still be minorly affected even below 108 kW.