I'm not sure but I think it improves the battery by letting it discharge all the way before re-charging. You may want to consider that.
No. In fact, discharging a Li-ion battery fully does much more harm than leaving it plugged in. It is best to charge your phone no lower than 10% if you can help it.
Here is my post on a previous battery discussion:
In the old days of nickle cadmium batteries, there was a necessity to properly condition the battery and then run it down, etc. With Li-ion, that is no longer the case.
The best example I can give is to imagine you are a product manufacturer and you need to put in a HUGE Li-ion battery in your product. You need the battery to last at least 10 years and go through thousands of cycles. The battery has to work in sub-zero temperatures as well as a hundred degrees. Of course, I am talking about electric vehicle batteries.
The amount of testing that these Li-ion batteries went through was much more than any laptop or cell phone manufacturer would do. A few interesting things were discovered: Cold makes no difference on the longevity of your battery. Cold simply makes the battery less efficient. Heat, on the other hand, is a battery killer. Li-ion batteries are most comfortable with the same temperature we are: around 72 degrees F.
In the past, we thought that running down a Li-ion would result in more cycles (or charge-deplete phases). In actuality, it was found that bringing a battery to below around 10% actually depletes battery life, as GSXR150 suggested. Keeping a Li-ion battery topped off is better than constantly depleting it. Of course, the best alternative would be to unplug the charger at full charge to keep from creating heat or unnecessary charging. However, keeping it plugged in is less detrimental than letting it deplete completely.
As to your specific question, running the battery before charging it fully is of no concern. The very out-dated nickle cadmium had a memory effect, so it was necessary to discharge these batteries. Starting with nickle metal hydride, there is no concern over memory, so there is no need to fully charge or discharge the battery, and with Li-ion, it can work to your disadvantage.
The nice thing is that if you ruin your battery because you abuse it, the replacement will only cost you $10 to $25. You abuse an electric vehicle battery and it will cost you around $5 to $10K.
