How accurate would be the following conclusion on 'Critical Temperature'?
Ok, I added a point Z to the diagram which I've added below, and I'm going to quote you text in italics below the image...



Just consider any point in the Pressure-Volume isotherms of $\ce{CO2}$ given above, which is in the region of gas-liquid equilibrium (within the shaded dome shaped curve) but has a volume greater than the critical one. For e.g a point that lies:


Within the shaded region. and
On a line passing through B and parallel to the pressure axis.


Let that point represent the state of liquid inside the vessel.

Question 1 - My point Z meets your two conditions doesn't it?

... From there if we increase the temperature, we would arrive at a point on the boundary of the dome shaped curve, (viz. B) but that point would be on a lower isotherm than the critical isotherm.

Assuming you agree with point Z, I agree with the idea above. The next two sentences is where you're wrong. 

And it looks like B is also a point where the two densities becomes equal.(isn't it?) Based on that premise, we can't say that the temperature arrived at in the above (heating liquid in a closed vessel) situation would necessarily be the Critical temperature. 

Let's start at point A, and follow the purple isotherm. At point A all the carbon dioxide is gas. At point B all of the carbon dioxide is still gas. But as you start to goto point C from point B the carbon dioxide vapor becomes supersaturated and liquid carbon dioxide forms. Now when you get to C there is so little volume that all the carbon dioxide is liquid. Thus only in the blue shaded area under the curve do you have two phases gas and liquid. 

Liquid carbon dioxide is denser than gaseous carbon dioxide. So the gas will be on top and the liquid below.