[Sci-Fi]

From 10W40:

Powershifting is effectively shifting without fully releasing the clutch. You keep the gas pedal down while you only use about half the clutch travel to shift hard and fast. This is incredibly hard on a transmission, and in fact simply will not work on most transmissions. Without fully pushing in the clutch on most cars, you can neither pull the shifter out of gear nor put it into a new one (and it will grind as you try).

From LS1.com:

Question 1-10: What is powershifting?

Answer: Powershifting is when you leave the gas pedal all the way to the floor and quickly move the shifter and work the clutch while racing. This allows a continuous application of power with no lag, and is typically good for a tenth or two improvement in the quarter mile times. It does not seem to cause any extra wear on the transmission either, the T56 transmission can take a lot of abuse.

http://www.zr1.net/ZR1_powershifting.html

IMHO, shifting without using the clutch, especially on a cable operated shifting transmission is not a good idea. Might be ok when selecting a lower gear at the correct or matching rpms, but it is very hard on your synchos if you constantly jam/force it into gear at the wrong rpms. You would need to modify the synchos, like grinding off every other tooth or finding somebody that can make up some racing synchos for you, to give you some margin for error. Otherwise you just might find yourself with a non-syncho transmission, or only a few working gears, with broken syncho parts floating around inside and learning on the fly how to double clutch just to get home.