It will be OK- as long as the total AMP combined from all the LED you use does not go over the rated AMP of the power supply...so in turn more amps means you can hoop up more LED's! yaaa! just dont go over the rated voltage of the LED. 12volt = 12volt. Have fun
So if your strip is a 10watt strip for example you calcualte it like this
10watts / 12 volts = 0.84Amps!
so in theory using a 450Watt power supply at 12Volt you have 37.5Amps MAX! But a computer power supply has several phases so that is split into 5volt/12volt per phase - and the phase max amps is always written on the PSU.
You also need to make sure that the LEDs input range is 12volt. They can vary form 3,5,9,12Volts respectively and need to be wired in series if lower that, or hooked up to a resistor; other wise it will glow, turn red.. and stop working. It will not short out- but the LED might get very hot and even smoke a bit if you over voltage it.
You can also use the 5volt line if your LED's are of lower voltage inputs.
A Computer power supply is one of the best to use as like you mentioned-- it has a very very stable 12/5volt supply. Which is important in electronics like hard drives/motherboards/ram etc.