Yes it will slow it down
Simple electric theory, Ohm's Law
Let's say your 12V 92mm case fan draws 1.0Amps at full load.
V=I*R where V = Volts, I = Amps, R = resistance
therefore R = V/I, R=12/1 = 12 Ohms
Also, P=V*I where P = power in watts, 12*1 = 12 watts of power
change it to 7, resistance is constant therefore
I=7/12 = .583 Amps
Power = 4.08watts
So the power of your fan at 7 volts is about 1/3 the power at 12 volts, therefore it will turn slower. How much slower depends on the construction of the fan.
I've also just run fans between Red and Black (+5V to ground) although some fans won't have enough power to spin up since in the above example it will only have 2 watts, or 1/6 the original power.
I guess some power supplies wouldn't like the 12V to 5V (net 7V difference) since you would be putting current back into the 5V line rather than to ground. The actual amount of current is pretty low though. If you are seriously worried about it just purchase a fan speed controller which will give you much more control over the fan speeds, from full blast to as low as you want. It is also a much safer way to do it if you don't know much about electrical systems as there is no cutting, soldering, or moving wires in connectors.