Loosely speaking, yes. By 'feel each other's Coulomb potential' you mean that the behaviour of one electron is influenced by the presence of the other owing to electrodynamic effects. That is undoubtedly the case. If you were to model the behaviour of an electron in an atom by considering only the potential due to the nucleus and electrons in other orbitals you would calculate imprecise answers. To help you visualise the reasons, imagine two atoms, identical except that one is ionised by missing an electron that would normally fill an orbital; clearly the two atoms appear different to an electron passing by, and the difference must be attributed to charge effects.
To try to illustrate the point from another direction. Suppose that an electron in a given orbit did not 'feel' the Coulomb repulsion from the other electrons in that orbit. In that case the electron would feel only the Coulomb potential from the nucleus. If that were true, then a nucleus would attract an infinite number of electrons.
Another illustration is provided by the Hartree-Fock method for calculating energy levels, in atoms for example. In that method, the Schrodinger equation is solved for a single electron by considering a Hamiltonian that models the presence of, including the Coulomb interaction from, the other electrons orbiting the nucleus.
In truth the Pauli exclusion principle is a post-hoc rule to reflect the observed population of electron orbitals.