I would agree, you would probably be better off getting a wall transformer (like a cell-phone charger) for your needs, they're pretty inexpensive and should deliver about the same level of quality power (it will have some ripple, turn on transients, etc compared to a lab power supply).
However, I think you are asking if the PSU will force 15A to your load; electrically that is impossible, voltage=current*resistance, if you have a fixed voltage and a fixed load, then the current will vary based on the two. 12V/ 20kohm = 0.6mA; conversely 12V/.1ohm = 120A = smoke machine.
The 15A simply means that the PSU can source up to that amount before it starts having problems (sagging voltage, overheating, or damaging components).
As noidea_77 said, don't try to source to much current over one wire. Too much current in a wire will generate a lot of heat and melt the insulation on the wire.
And seriously, be careful, a computer PSU handles a LOT of energy, if you aren't careful you could seriously hurt yourself (also don't open the PSU for any reason, the caps inside are large enough to kill you).