Will this MOSFET switch circuit work?
Correction to the schematic: your IRF530 is installed backwards. You don't want the body diode "pointed" in the same direction as your LED string. The N-FET source terminal should be connected to the negative terminal of your 12V supply.

While using a LMx24 as a comparator isn't the best, since its input common mode range and its output range includes the negative/ground supply and the threshold voltage of the IRF530 is at most 4V, this circuit (with the corrected FET direction) will mostly work if you use a LM7805 or higher voltage (accounting for dropout, 5 to 9V should be a reasonable choice of 78xx). From the comments: remember that the IRF530 has its on resistance rated at a \$V_{GS}\$ of 10V. Acceptable performance may be found for this application at lower gate voltage, but choosing a different FET with a "logic level" gate drive capability would help if a 7805 is used.

However, your op-amp (being used as a comparator) has no hysteresis. This means that at certain light levels, you will have a flickering LED string because your threshold potentiometer and the LDR/resistor divider have almost the same outputs. For some good information on why you want hysteresis and how to implement it, check out TI's TIDU020A document. The difference in their circuits is: