Yes, leaving it open is actually very detrimental to cooling. Granted, there will be more air for the fans to push, but it wont be directed in any specific direction. They will blow a lot of air everywhere, resulting in lower cooling. If you have a closed case, the air really only has one directionto go, and that is in the direction that you set the fans to move it in. Ideal air flow is intake on the front, and exhaust on the back. It's not just the buildup of heat inside the case, it is alot to do with the moving of heat from the heatsinks and other parts to outside of the case. Removing any heat possible from a case is what you want to do. You have lots of little things that give off very little heat. REsistors, tiny SMD ones, MOSfets, capacitors, etc... While they each would give off less than 1/100th of a watt of heat, lets say for pusposes of this that they each give off 1/100th of a watt, thats not very much. However, when you have HUNDREDS of resistors and several mosfets and capacitors all giving off heat, it adds up.
I read an article years back on Toms Hardware about watercooling, like I said above. They wanted to try to make a entire case JUST water cooled (No fans whatsoever) and it would work for a little while until heat built up in things, and then it would start to crash. They put one fan in there, ONE, and it stopped crashign. If one fan makes that much of a difference, imagine what several would do.
In conclusion:
More case fans = Good
No case fans = Bad