An atom made of hydrogen is a combination of an electron and proton in a bound state. Given these two components, there is only one type of bound state.
Non-relativistically, the two-body problem is separable into center of mass motion and relative motion by a simple coordinate transformation.
The Schrodinger equation at the relative coordinate becomes an equation for one electron with a reduced mass that is attracted to a fixed centre by a Coulomb force. This is because the electron mass is so close to its reduced mass that it is almost impossible to mention this detail.
The Schrodinger equation at the center of mass coordinate gives the free particle motion for the atom.
Non-relativistically, there is no difference between the two atoms you propose. Both are hydrogen atoms.
They will interact in the same way as normal hydrogen atoms.
We use the term electron shells to refer to atoms that have nucleus. The nucleus is much heavier than electrons and therefore moves about a lot less.
Although the situation is more complex mathematically, it is still the same: A hydrogen atom is a binding state of an electron or a proton. It doesn’t matter which one you choose to say is in what position. This bound state is still a hydrogen atom.
Dark matter is not hydrogen atoms nor any other ordinary atoms. However, it is an appealing possibility. People believed dark matter existed in the form brown dwarf stars orbiting around galaxies for some time. However, this would have implied gravitational lensesing effects that were not observed when searching for it.
Hydrogen molecules would be better. H2 is difficult to see around galaxies because it can be so cool and invisible. However, all estimates of the mass of H2 indicate that it isn’t enough to account for the dark matter.