Removing it does basically nothing. It doesn't affect flow at all, since the air is just passing over the opening for it and not directing through it. If you were able to make the intake totally smooth there you may help the intake flow a tiny amount better due to the less turbulance introcuced by the smoother intake wall. But just capping it doesn't change that. I'm not 100% sure why it is there, but my guess is that the turbulence of the air in the intake was causing to to resonate at a frequency people could hear, and the aditional box there changes the air volume and therefor the frequency of sound it would produce. It may also serve as a water trap for rain that has made it's way up the intake tract.
There is also a tube into the box that sits on the valve cover and attaches to the throttle body. Many people remove this and claim more power. All it's really there for is to keep the intake quieter and also direct flow a little better towards the throttle body. I removed mine and found the intake to become much louder, but no power gain. In fact, I seemed to have lost some power after doing it. There is a large hill heading out of town that I can hold about 50mph up floored in 4th gear (I usually just cruise up at 40 mph in 3rd, that's the speed limit anyway). After removing the tube I found that floored in 4th only mustered 45-47 mph, opposed to the 50 mph on the dot that I had always gotten before. Plus it was a hell of a lot louder while doing it. I put the tube back in.
One place I did notice a difference was hacking up the stock airbox. The small front snout is very restrictive, I basically cut the front 1/4 of the box off so there is much more room for air to enter now. That, along with a drop in K&N gave me a small amount of noticable power, plus a small (~1 mpg) gas milage increase.
The problem with the stock intake is the 100 mile long track of bends and turns and accordian tube the air must travel. The box isn't really restrictive at all once modified, but there needs to be a straight shot from there to the throttle body for a real difference in power. I'd like to get some tubing bent up someday to utilize the stock box (just to try it). But for now I am sitting on $2 and can't afford it (college priorities, rent, food, truck payment, beer, err, something like that).