You can find volumes of info about this but here's the brutal truth. Batteries age even when unused. While you could charge it and then place it in a plastic bag with desiccant in the fridge (not freezer) this negates all the reasons for having a battery.
So no, that is not considered a full cycle. The terrible truth is the common laptop battery is a 18 or so month life span thing with 300 or so good cycles. If you don't need a battery, remove it but then where is the benefit of the battery?
As to the cycling, that's been discussed too many times and as you will discover the battery technology makes a difference. For the most part you can just leave it fully charged on the desktop and it will last a long time. We have laptops on the desktops and the battery works 2 years later. And they rarely ran on battery alone.
I recently purchased a Dell Studio 14z and im really enjoying my laptop. In fact, switching from my old laptop which's battery would last no longer than a few minutes has really been nice. However, im worried that I may be using the battery in such a way that the life will be shorter then it should be. I know that the lithium ion batteries are not like the old ones and do not need to be run down or can be over charged, but rather have a certain number of charge cycles. I find that Ill use my laptop on battery power for a discharge anywhere from 5% to 25% and then put it back on the charger. Is this short discharge counting as a charge cycle? Should i run it down lower before charging? Any help would be greatly appreciated! Thanks!