Help! Important Question Needs An Answer

Take Einstein’s classical General Relativity in its full mathematical glory with everything exactly as Einstein, with the help of others, published in 1915 or 1916.

But leave the constant G undefined. Einstein put in the Newtonian G because it gave the right answers for the tests he envisioned, like the advance of the perihelion of Mercury. Without G being defined, i.e., chosen, all the terms in the full GR equations have their intended dimensionalities, but there are no units or quantitative magnitudes in the equations or in its solutions.

Is this correct, or is there a flaw in the simple argument. If it is true, then GR without specified G has global conformal symmetry, or at least the conventional symmetries + dilatation symmetry. As such, G would be a likely point of attack for how to make GR conformal. If G is not an absolute constant then some interesting possibilities arise.