Dan - welcome. I'm assuming, since you posted in this thread, that you live in Suffolk County. If that's the case, it is legal for you to have a pistol in your home only with a pistol permit. I'm guessing you already knew that, but just making sure. With a permit, there is no legal problem with keeping the pistol loaded. Of course, use common sense when decided how to store your firearm. There is currently pending legislation in NY that would require handguns to be stored empty and locked, but in light of DC vs Heller, I'm hoping that won't go anywhere.
As far as the 24-hour range thing, keep this in mind: the SCPD issues permits with target/hunting restrictions. Those restrictions authorize you to carry to and from the range and to and from the field. SCPD recently deleted from the handbook the provision allowing permit holders to stop for refreshments on their way to/from the range. So your permit authorizes you to carry only to/from the range - no pit stops. There is no LEGAL problem with it - but there is a problem in the eyes of the SCPD, and they may see fit to yank your permit, should they find out. I'm not saying I agree with their policy, and I'm not commenting on what members of this forum chose to do, or not to do. I'm only pointing out that as Peetza said, it makes me a bit nervous that you may be thinking about how to skirt the limits of the law before even getting a permit. Keep in mind that the internet, and this forum, is a public domain - viewable by law-enforcement and by anti's who have their sights set on gun-owners. I don't think anyone here would condone violating the SCPD restrictions, regardless of out personal convictions or actions. As Peetza said, we should be inclined to act like the upstanding citizens that we purport to be - espeically as we're increasingly scrutinized.
In any case, please continue to post - there is a wealth of information here, and I'm sure everyone will be glad to give you whatever help they can. Good luck on getting your permit!!