A photocell is the same as an LDR, just a light sensitive resistor as you say. However, if you set it up as you propose, it'll drain the battery pretty quickly. Also, you have to calculate the resistances and switching points carefully (the switching on current of the relay) and the switching point will change as the battery gets more drained, not to mention that the relay may have a lower switching off current than you get with the laser pointer turned off, so it may not break contact after making contact.
You really should use some form of low current drain switching electronics, especially if you want to run it from a battery. As I said, you could use a couple of transistors to do it like this instead:
But it's not as efficient as the comparator. The circuit I provided has only 4 parts, is simple to make and runs from the existing PC lines, so you don't need a battery. The +5v VSB line from the power supply (standby voltage line) is always on, supplying 5v to the motherboard so it can handle switching the power supply on when the button is pushed. You can use any ground connection. You could of course also use a battery if you don't want to play with the pc power supply connections.
P.S. - Photocells are most sensitive to green light, less to other frequencies, so a green laser pointer is ideal.