Yes with an open air box you could expect more hp as well as more noise. Both of those elements are great. The great thing about the "open air box" is that you hear the engine howling out of the air intakes. Here are some ways the air box can be "open"
1. Lift your gas tank and you will see this plastic box with two trumpets portruding from the top. You may remove those.
2. This plastic box's top is held on by clips. If you un snap the clips the top of the box will come off and inside you will find your air filter. You may cut out the middle part of the airbox leaving only the bottom of the lid so that you may fasten the lid back to secure the air filter.
3. You can totally remove this lid and just have the air filter totally exposed. This is the way I ran my bike. I thought it worked very well. Some members have some reservations about doing it this way due to water being able to enter the air box, though I never had any problem with this, AND the bottom of the airbox has a collector and a drain just in case water got in there. Though not very good, here is a picture of my air filter taken from the right side of the bike looking toward the front of the bike.
4. The most advanced way to do this option, which most do not take to, nor helps that much over a true exposed air filter is to delete the whole air box and mount air filters right to your intake mechanism (carb/throttle body) I just did this mod today, and it is mainly for looks, but here it is anyway.
As you go down the list of suggestions, the "potential" for more horsepower increases as each suggestion suggests a way to let more air into the engine. The more air a engine can receive the more power potential it has to make.
The best thing about the "open air box" is that each owner can do as he pleases and will be happy with the results. If you don't want to take your air box lid all the way off, then don't just cut the lid, or whatever, its your bike you decide how you want to modify it.
One last thing is engines need to key ingredients: Air and Fuel, so if you increase one of the two ingredients you need to also increase the latter as to keep them in equilibrium.
-Patrick