Sure, cool battery is much better than hot battery. But it has nothing in common with using a battery straight from a charger (if it was not heated in it). But battery can became warm in a mod quit soon, so does slight temperature rise due to charging really matter?
In my personal opinion, as long as the battery is just a bit warm...no. Not to any practical extent that we'll ever see.
If the battery comes off the charger at 35°C (versus 20°C if left to rest), and its use in a mod increases its temp by 50°C then we have a 85°C battery temp versus a 70°C temp. On paper, yea, that higher temperature means more damage. For us vapers I think that difference is tiny though compared to all the other abuse we put our batteries through.
If the battery comes off the charger very warm or hot then there could be problems if the battery was being used at its max limits in a mod. I think that's the biggest reason why there is a general warning to always let the battery rest after charging. There's always going to be someone who charges a battery too quickly and then tries to fire a 0.05 ohm build with it.
[edit] There are changes that are still taking place inside a cell after a charge finishes, e.g., the ions are still redistributing themselves equally across the cell. While I cannot see it helping a cell by using it immediately, I do not know how much doing this would accelerate aging. I do not know if these changes are completed when the cell comes back down to room temperature or not.