To do this I would need to be able to find out the helicopter's pitch angle so I could adjust the height at which the camera looked at the game logic unit thus matching the helo's pitch angle.
Thats possible, the easiest way (as usual with OFP there is more than one way to skin a cat). Take the Height Above Sea Level (Vektorbosons function will do this, among others) of the Helicopter and It's Pilot, while placed on flat ground. Calculate the angle between the the heli and the pilots position and store this as an offset.
Then while in game, repeat the process but compare the result with the offset you recorded earlier. That will give you it's pitch (or bank) relative to the horizon, at any point in time.
This will work ok most of the time, a few things conspire to give you false readings for Height Above Sea Level. But assuming you wont want your camera to swing about to wildly, I'd just cap the values you use to move the camera about.
BTW What heli if any specific one, do you want to use this with?