The practical difference between having the plane 'exactly' straight & level, and having the nose down a few degrees, is pretty small. The absolute error woud depend on how big your model is, and how far inside the fuselage the three-dimensional balance point is. (Which in most cases we don't know.)

Consider this: if your model is hanging nose down by five degrees (which is way down, from a visual point of view), and you have a big model, let's say a Cub, with 12" height from bottom of fuselage to top of wing (where you have your Desired CG marked), and if the center of the overall mass of the model is vertically halfway in the height dimension (probably close to that in most models, a bit lower for a low-wing type), then the error resulting from not being straight & level will be about a half-inch. (I worked it out; if you know trigonometry, you can check me on that.) The good news is, the actual, physical balance point will be forward (i.e. on the stable side) of where the indicator (plumb bob) is pointing.

My PT-19 flew with its tail way up. Lots of scale planes are configured that way, so that when you add throttle, you not only get more power, but the plane climbs by itself.

So what I'm saying is, if you're hanging at what looks like nose somewhat down, just know that your CG determination will not be far off, and the error will be on the side of safety. As someone pointed out above, all you're after in this initial stage is coming up with a safe CG for first flight, after which you will move the CG based on how it flies, not how it hangs or balances on your machine.

This points up what is to me the real advantage of the sling, which is facilitating the quick and dirty balancing involved in placement of heavy components (batteries & servos) so you get close to final balance without using lead ballast, or very little of it, one hopes.