I think you will for this reason: once you have rejetted to compensate for the increased airflow, you will be burning a significantly larger amount of fuel, hence making more power.
It's kinda funny, I never actually ran mine with the lid, but a couple of weeks ago I had put on the lid for washing (it does keep water out nicely) and forgot to remove it again before riding. WTF, I thought. It would barely run and immediately fouled the plug. I put in a second plug and fouled that too before I realized the problem. What a huge difference in airflow.
So, the moral of the story I guess is, yes it is a huge difference as long as you jet properly to compensate. Do not run without a lid until you are prepared to rejet. (It is a recipe for a burned piston)