Well, kinda, and, I think close enough.

The NP of the airplane can actually change in flight (depending on the airfoil), but it's reasonable to think of it as fixed.

The nose-up/nose-down thing, while not inaccurate, is not the way I'd describe it. Nose up/down only applys when you're suspending the airplane on your finger tips or a balancer at some arbitrary point. If you pick a point far enough forward, the plane will always go nose up, and vice versa. When I check a plane's CG, I try to find the point where the plane balances level. That tells me where the CG is at the time. Then I look at where that is in realtion to the wing chord, and where I'd expect it to be (25-33% of MAC to start with).

Once the plane has flown, I adjust the CG by moving it a little bit at a time, again finding the point where the plane balances level. Depending on how the plane flew, I'll usually move it 1/4" at a time or so (depends on the plane of course). The problem with suspending the plane so that it's nose-down or tail-down is that you then have to worry about the angle. It's easier to always balance level, mark that balance point, and measure it's location.

In the air, flying nose up or down depends on a lot of factors, the CG just being one of them.