The short answer to your questions is...NO.

Now for the long answers...

From the practical standpoint, at depth (before you start ascending), you should be neutrally buoyant. To start your ascent, you can take a deeper than normal breath to get a little upward motion. As you ascend, you should be dumping some of the air as you go up. At any point, during the ascent you should be neutral.

From the safety standpoint, any air you add to the BCD will expand; therefore, making you more bouyant. This could lead to an out of control ascent. Plus, if you add air, you then have to dump the air. Personally, I would prefer to use my air to breathe.

The only time you might need to add air is if you are negatively bouyany at depth. You will need to add air to get to neutral. From that point, go back to my first "long" answer.

Also, common practice these days state that ascending 30 feet per minute should be the fastest you go. Some training agencies still train 60 feet per minute. The "no faster than your bubbles" hasn't been taught in a long time.