How to determine the practical constant current rate of charging phase of a Lithium battery?
At the moment the terminal voltage of the battery is just reached to
  the CV value (4.2V for Li-Ion), increase current limit of the power
  supply to the point that the actually drawn current is not increasing
  anymore.


At this point the battery has reached maximum voltage and current is already throttling back from the previously set limit, so raising the current limit will make no difference. So no, it wouldn't work.

What could work is watching the rate of voltage rise earlier in the charging cycle, and adjusting the current until the voltage rises at the expected rate for that part of the cycle. Now the only problem is, what is the expected rate of voltage rise? If the battery is rated for charging at 1C then it should reach 4.2V per cell in about 40 minutes, and you could adjust the charge current to match the curve in your graph. 

However an old battery (with higher resistance) or high capacity battery (rated for lower charging current) should take longer, and that would have to be taken into account. Perhaps the charger could measure the battery's internal resistance, and adjust the charge current to suit.

Today I charged an old high capacity Lipo battery that had not been recharged in over 2 years (it gets used infrequently at a low discharge rate). The battery had no markings to tell me what rate to charge it at, but knowing that it is designed for a low rate I started at 0.5C. The voltage climbed up to 4.2V in a few minutes, which indicated that the current was too high. After cutting back to 0.1C the voltage finally settled down to what I was expecting. If my charger did that automatically I might think it was faulty! But that is the correct charge rate for this old high capacity battery.