Think about what happens with a simpler value for G(s) such as a 2nd order low pass filter formed from an inductor and capacitor. In open loop you have this circuit: -
And the phase and gain response is like this: -
At DC there is no phase shift between output and input. At resonance there is 90 degrees of phase shift and at high frequencies you tend to get 180 degrees of phase shift but with very little output signal.
This circuit on its own cannot oscillate and, even if you put it within a feedback loop there will never be enough phase shift to produce oscillation. It could however produce over shoot like this: -
But it won't be sustained i.e. it will die down.
However, your G(s) has an integrator cascaded with a 3rd order low pass filter so it could definitely oscillate if you don't control the feedback.
Consider the 2nd order RLC circuit above. If you added a phase shift of 90 degrees by cascading the RLC circuit with an integrator and "closed the loop" then it would likely oscillate close to resonance because at just past resonance the phase shift will be exactly 180 degrees and the gain (|G(s)|) could be greater than unity.