It is certainly possible, but you need to open your PS2 and that will invalidate your guarantee. Also you will still need to purchase some "swap magic" discs. "magic keys" or "slim tools" are cheap and can be used alongside "swap magic" to allow you to play copied games without the need to open your PS2.
If you don't want to spend out for "magic keys" or similar (highly recommended), then you can do this simple modification to your ps2:
Take apart your ps2, Right of center at the rear of the mainboard, you will see a microswitch that gets pressed when you close the flap. Stick some tape or blue-tac over this switch to keep it pressed in. Next, look for the little circuit board that is right behind the power button. on this board there is another microswitch that gets pressed when you close the flap. Solder some small flexible wires to the two switch contacts. Then fit a small toggle switch to the PS2 (SEE PIC) and solder the wires from the microswitch to it.
When the new toggle switch is off, the playstation behaves as normal, but when it is on it overrides the microswitch, allowing you to open the flap and with the use of Swap Magic disks, play copied games.
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