Can a system with more than 180 phase lag ever be stable?
At first, some clarifications:

1.) It is the loop gain (open the loop and measure/simulate the gain of the complete loop) which is subject of this stabilization criterion you have mentioned (if the loop phase reaches -180deg the loop gain must be &lt;1 already).
If this criterion is fulfilled, the closed loop is stable.

2.) However, this criterion applies only to a system where the critical phase (-180 deg) is crossed only once! Otherwise (when the phase goes again above this critical line) you must apply the Nyquist criterion to check stability (which might be a "conditional" stability only).

3.) Regarding your last example: The loop gain criterion (first point) applies to a 4th-order system as well. No - it does not help at all to "limit" the frequency.....