Dear Avinash,
Coming to your case, firstly DC gain is only effected by the output load which causes an effective resistance of less than r0 to ground. Remember at DC, the gain is gm*(r0||RL). In your case, I do not see any direct path to ground. It is through a switch(which has very less resistance) and a capacitor. Hence there is no direct RL (of the switch) which can reduce the DC gain.
Well coming to the GBW, I meant to say that instead of a simple pole at the output in the form of Capacitance, you now see a load of Switch ON res and a cap in series as load. This will cause a LHP zero in your Magnitude and phase responses. So, stability might be critical in the sense that there could be damped ringing. You need to size the switch such that, the LHP zero is outside the clocking frequency of the switch.......