Per the FAA? Sure, just give between 1 and 24 hours warning to the nearest FSS, make the call before you jump and go. Has to be uncontrolled airspace (class D or E) which can be hard to find near airports. You also need permission of the landowner. And of course you need to have a pilot who is willing to take you and an aircraft that can fly with the door open.
It would also be very, very smart to have a PRO rating before you try to organize an impromptu demo.
Has to be uncontrolled airspace (class D or E) which can be hard to find near airports.
Class D and E are both controlled, but VFR activities such as skydiving are allowed.
Class D airspace is within a 5 statute mile radius of an airport with a control tower, up to 2500' AGL. Permission from the tower is required for parachuting activity.
Class E airspace in just about everywhere else. No permission is needed, just contact ATC for traffic advisories prior to each jump.
Class B airspace, around major airports, requires all kinds of special permission. We jumped in Class B airspace for years. I have story or two about that. Any good pilot should know the type of airspace his flight is in and who to contact for air traffic control services.
Not knowing your experience level, or the situation in general, I have a few comments.
First off, make sure the pilot is qualified. A 'new' helo pilot might not be the best person to use as a jump pilot. It's an unusual situation, with an open cabin and rapid weight shift/change, and an addition to the workload. Not the best idea for a 'new guy', maybe if he's a commercial helo pilot, that would be a good indication of training, skill, and expereince.
As for the jumping, again, not knowing your experience, being on a DZ surrounded by staff and other jumpers has it's benefits, none of which you will have jumping off-site.
Things like spotting, and LZ selection. Having an extra set of eyes on your gear, or being able to get a gear check/pin check at all. Having a 'crowd' of people watching your landing and responding to you if you are injured. Ditto if you have a mal or land off, all of those jumpers on the ground will be able to get a line on where you and your gear lands, and be able to recover both much quicker. If you happen to land off and be injured, that response time is all that much more important.
Again, just some generic things to think about when jumping off the DZ, or with non-jump aircraft or pilots.