Mike:
No. You missed that it is the relay coil that is in series with the switch, the combination of which is across the +12 volt supply. The relay coil has some resistance to it and this limits the current to some finite amount. Say the coil was 120 ohms then the current would nominally be limited to 12V/120ohms = 100mA when the switch is closed.

Of course there could be situations where the +12 volt supply comes from a low current source such as a LM7812 that may be current limited to 1A and the relay was come type of huge contactor with a 2.4 ohm coil in which case the current draw through the coil would be more than enough to swamp out the supply and limit the source so that it outputs decidedly less than +12 volts.

Michael Karas