No, the rider's weight is taken up by the axle threads in contact with the dropouts. Look at your dropouts and you'll see scoring where the axle threads make contact.
That may be the norm but it isn't necessarily so I had a bike which had a slight mishap and if the axle was put in the correct place in the dropouts the wheel didn't run true. It had to be out of position on one side but it ran like this for years without the axle touching the dropouts on one side and relying on the friction of the QR dobbie to hold it in place - The QR was no tighter than normal
