Kinda sorta. As fsh responded elsewhere in the thread, the difference between the antiproton and an electron is that the antiproton can annihilate with one of the protons in the helium nucleus (since it's an exact antiparticle of the proton, whereas an electron is not). The probability of this annihilation happening per unit time depends, roughly speaking, on how much the antiproton's wave function overlaps with the wave function of the protons in the nucleus, which in turn depends on which orbital the antiproton is in. But the overlap will be nonzero in any orbital, which means that this configuration is kind of like a radioactive atom: the question is not whether it will decay--eventually it will--but how long it will take on average. The "half-life" of the antiproton configuration in this experiment was on the order of microseconds, which is quite long for an antiproton.
For only one electron or one antiproton, the orbitals have the same shape and classification. The only difference is that the size depends on the mass, so the orbital to put the antiproton are much smaller than the orbitals to put the electrons. Note that something similar happens with muons that have an intermediate mass and the orbital to put them have an intermediate size. https://en.wikipedia.org/wiki/Bohr_radius
It's more difficult when you have many electrons or muons or antiprotons. (I guess nobody had measured a system with many muons or antiprotons.) If you have many electrons, the problem is that you must calculate the attraction of the nuclei and the repulsion of the other electrons, so the orbitals change. In particular, the filling rules https://en.wikipedia.org/wiki/Electron_configuration#Atoms:_... don't follow the energies of the orbitals of an isolated electron.
In a system with many muons or antiprotons, all of them will be closer and the repulsion will be bigger, and I expect weird filling rules.
Electrons: 1s_up, 1s_down, 2s_up, 2s_down, ...
¿¿¿Antiprotons: 1s_up, 2s_up, 1s_down, 2s_down, ... ???
It is possible to calculate the filling order for muons and antiprotons numerically, but I'm too lazy do do the calculation now and also the standard programs [1] [2] have a lot of hidden assumptions to make the calculations with electrons more efficient and I'm not sure how difficult is to tweak the entry files to calculate this fast enough. [3]
[1] https://en.wikipedia.org/wiki/Gaussian_(software)
[2] https://en.wikipedia.org/wiki/PSI_(computational_chemistry)
[3] Perhaps it's implemented and I just need to RTFM, but otherwise it looks too straightforward for a PhD thesis, but it may be a nice undergraduate thesis.
An electron is bound to the nucleus by the electromagnetic force, but is not a round ball, but a wave distribution of probabilities.
I don't know if it's the actual case, but I've been thinking of all "particles" like "waves" in a pool. Small disturbances in the fields (e.g. electromagnetic), like jumping in a pool. The electron IS the disturbance, because to us that is what we can measure (and we can only measure one place at a time). So the electron doesn't rotate around the nucleus - instead its a wave in the same area where the nucleus is. The electron's "probability wave" disturbs the space around the nucleus - including inside it, and 1000 miles away from it. It's just has way more disturbance in certain places - AKA "the shell" its in. Just like any wave, it "fades" with distance but who's to say where the wave ends.
In fact, that wave isn't exactly the same for every electron. Each "shell" is waving at a different amplitude (is amplitude the right analogy?) - and you can only have so many "waves" add up in a shell simply because there's no more room because of the length of each wave (like a spiral-o-graph). You can only put another wave in the gaps of the previous wave (if you did put two in the same place, it would double and be part of the next shell, right?). And when an electron's amplitude changes, e.g. is lowered, the total energy can't be destroyed, so the difference is emitted as another wave of the difference - that wave is a photon. And the same applies when a photon is added to that wave. Like rowing in the water - the exiting wave and the rowed wave is added together. I think of Photons are partial Electrons. They are like the "wake" of an electrons wave change.
In an atom, the electron state energy comes from the electric potential energy due to the electron's charge sitting in the electric field produced by the nucleus. The further out the charge is, the higher the potential energy (and hence the lower the binding energy). This is distinct from the electron amplitude. The electron amplitude is essentially how much electron is present at a point, and lowering it violates conservation laws (lepton number, mass, charge).