I dont think that it improves neither
the input common mode range nor the output
common mode range (Because if you stat decreasing the common mode voltage of both
input will results the tail current transistor to enter
to triode region at the same drain voltage).
If we have purely differential signal, we should
expect the gate terminal of the M3 should stay
at the same voltage, which is input common mode voltage). Now, it the differential voltage is zero
that the tail current will be shared by these three
transistor equally. When a differential signal applied
the current of M1 will decrease & M2 will increase, whereas the current of M3 will stay all most the same (first order) which dictate a constant voltage drop from its gate voltage (input common mode voltage) to source terminal (common node). Hence,
this structure will decrease even further
the impedance on common mode for small signal and even so for large signal. Now the impedance
on that node is important for 2 reason
first is the common mode rejection ration, because
the modulation on the common node will result
a bias current modulation through the output resistance of the tail current, and the switching speed of the diff pair especially for slewing conditions. I would expect that it improves the
common mode rejection ratio, and somewhat
slewing condition of the amplifier.