Mobile charging during low main supply
Phone chargers use switched-mode power-supply (SMPS) technology.



Figure 1. The block diagram of an SMPS. Source: Wikimedia Commons.

The chopper controller adjusts the chopper pulse widths to maintain the specified output voltage. The unit should work correctly across the specified range of input voltages.


  Can the charger to pull its required 800mA fod (sic) charging at this situation..?


No, the charger will supply 800 mA.

The charger will draw about \$ 800 \times \frac {V_{OUT}}{V_{IN}} \ \text {mA} \$ from the mains. So at 100 V this will be about 40 mA and at 200 V about 20 mA. Divide each of those by the efficiency to get a more accurate number.



Note, in standard English there are no punctuation marks or spaces before a question mark. Adding them in makes your post more difficult to read.