Will a 1hp hayward pool pump service 24000 gallons?

No. At least a 2Hp pump here. Also be sure your filter is large enough to handle the flow rate.

Yes it will, provided that you let it run long enough and your Plumbing is not too convoluted and your filter is large enough. You only need to get 17GPM, if you run the pump 24 hours a day. Most 1HP pumps these days can easily do that, even with 60 feet of head. If you plan on running solar pannels on a roof, then you will need 2HP.