If we have observed a closing of the excitation gap in the energy spectrum of a certain model, can we safely conclude that a quantum phase transition occurs?
No. For instance, you could have just touched a phase boundary and returned into the same phase. Or you could have a short-range correlated system (such as a Toric Code wavefunction) which can occur both as a ground state of a gapped and a gapless Hamiltonian (see e.g. https://arxiv.org/abs/1111.5817), and interpolate between those Hamiltonians -- this path would close a gap without the ground state changing at all.