Technically you could do that and the single resistor would be the same value as one of the resistors in the original design. If you did put in all four, which would be pointless in that situation, you would need each resistor to be 4*R.

Now for the reason you don't want to do that. Each LED will not drop the exact voltage, leading in one pulling more current than the others. As time goes on that may effect that diode increasing the current draw until premature failure. So in an engineering stand point you don't want to do that. My two cents.