Well, sort of. Yes, colder beer will absorb CO2 quicker. But that is just the first part of carbonation. The second part is the hydration of the dissolved CO2. Since it is a chemical process, I am pretty sure that it will proceed quicker when the beer is warmer.
I think that most of us recognize fresh carbonation. The bubbles are big and coarse, just like at the soda fountain. It takes time for the carbonation, that we can easily inject into the beer, to hydrate and produce those nice fine bubbles that we prefer in our glasses.
So it seems to be a balance between time and temperature for carbonation. In my experience, it still takes about 2 weeks to get the fine bubbles in beer. But you can still enjoy that beer with coarse bubbles in the interim.