Hi Damian,
This question was motivated by discussions of whether or not to deposit riding hydrogens in the PDB,
this was discussed so many times on both ccp4bb and phenixbb... So, very briefly, I do not know any single reason (and can't even imagine one) why one may want to remove hydrogens before PDB deposition. Most of reasons why hydrogen atoms should not be removed are listed in: phenix.model_vs_data: a high-level tool for the calculation of crystallographic model and data statistics. P.V. Afonine, R.W. Grosse-Kunstleve, V.B. Chen, J.J. Headd, N.W. Moriarty, J.S. Richardson, D.C. Richardson, A. Urzhumtsev, P.H. Zwart, P.D. Adams J. Appl. Cryst. 43, 677-685 (2010). and lots of hints here: Joint X-ray and neutron refinement with phenix.refine. P.V. Afonine, M. Mustyakimov, R.W. Grosse-Kunstleve, N.W. Moriarty, P. Langan, and P.D. Adams Acta Cryst. D66, 1153-1163 (2010).
So in the context of Phenix and Fcalc, do the positions of the riding hydrogens matter?
Yes, positions matter. As well as B-factors and occupancies. Note, B-factors of H are inherited from parent atoms with some multiplier that ranges from 1 to 1.5 (see SHELXL manual for details).
And if they don't, does this mean that when an input model has zero hydrogens, Phenix is still trying in some way to account for the unmodeled/invisible hydrogens that we know are in there?
No, if there are no H atoms in input PDB file, phenix.refine will not try to account for missing H in any way. Pavel