Maybe. Depends on what the page it is displaying forces it to do. A simple static page with text and few images causes negligible load, whereas one laden with Flash content and the like pushes the CPU thru the roof. Not to mention the popups and extra pages or tabs that some shady sites are fond of launching.
Another thing to investigate is what the Dashboard and its retinue of widgets are up to. Some may be continuously fetching data, like stock quotes, weather info, sports results, etc., hammering the wireless connection. Others may be computing stuff, like graphing the wireless performance, drawing a starry sky, etc.
Each may not amount to much, but when they all gang up on the poor unsuspecting Mac, results can be devastating.