It’s kind of a philosophical question, which depends on quite what you mean by “particle.” This particular language isn't common, and lots of people might have strong opinions that it's incorrect. However, a multi-electron composite state is different from a product of single-electron states in a number of different ways, and referring to the multi-electron state as "a particle" is a useful way to keep yourself from falling into some common traps.
A common situation where this language is useful is when thinking about emission and absorption of radiation by atoms. It's quite common to see language like
[misleading] The electron absorbs a photon and jumps to a higher-energy orbital.
The trouble with this statement is that a single electron can't emit or absorb energy. In hydrogen spectroscopy, the photons are emitted and absorbed by the atom, and the approximation that the nucleus remains stationary is just that: an approximation. For multi-electron atoms, it is useful to pretend like each electron is added to a hydrogen-like orbital, and to use the multiplicities of these orbitals explain the shape of the periodic table. (Orbital angular momentum states have odd multiplicities $1,3,5,\cdots$, which are doubled for the spin degree of freedom, so the different blocks of the periodic table have two columns, six columns, ten columns, fourteen columns.)
But only some features of the hydrogen-like orbitals are preserved in multi-electron atoms. The nucleus-electron-electron wavefunction for neutral helium atoms is actually too complicated to solve exactly, in the way that we have exact solutions for the hydrogen atom. And a consequence of this extra complexity is that, when a multi-electron atom (or ion) emits or absorbs photons, the approximation that "a single electron" jumps to a different orbital is likewise just an approximation. When a complicated atom changes state, its entire electronic wavefunction changes, in a way that we mostly can only solve numerically.
Another case where it's useful to think of a multi-electron state as "a particle" is in a superconductor. In a normal conductor, a useful model of electric current describes single electrons which scatter off of the nuclei in the crystal lattice and lose energy. However, in a superconductor, the conduction electrons form "Cooper pairs," named for the "C" in the BCS theory of superconductivity. A very handwaving way to think of superconductivity is that the two electrons in the Cooper pair scatter from the lattice in opposite ways, so the scattered states interfere with each other destructively and the entire material becomes transparent. But it's just as valid to think of the Cooper pair as "a particle," whose spin, mass, and charge are different from the electrons into which it will split at higher temperature.
A much more common case of a composite state being treated as a single particle is the nucleon (that is, the proton or neutron). At very high energies, nucleons undergo internal excitations which suggest they are "made" of "quarks." But at low energies, the quark-gluon degrees of freedom stop being useful for predicting the excitation spectra of nuclei. If I wanted to have a debate at a pub, I might argue that the neutron has a better claim to being a "particle" than an up quark does, because it is possible to build machines that spray mostly neutrons, but it is impossible to build machines that spray mostly up quarks.
You might also consider Gamow's influential cluster-tunneling model for alpha decay, in which "an alpha particle forms" within the complicated morass that is a heavy nucleus in its ground state, and then that alpha particle has some finite probability of leaking out of the nucleus. That model really does consider "an alpha particle" as a single object, rather than as a bound state of four nucleons.
Your quoted text seems to suggest you could describe a helium atom as a nucleus bound to "an electron spin singlet." I don't think that's very good language to use. But I would absolutely 100% consider "a helium atom" as "a particle," just as I do the alpha particle, and just as I do the two-electron Cooper pair.