Absolutely not. Read up on task killers, there are tons of threads on here about them. Android works by keeping its ram full of apps. Those apps are NOT running, just cached. When you kill those apps, no matter how often, android sees that open ram, and will load all of those apps back into cache. Thus making the phone and battery work more than if you just leave it alone. Not to mention problems caused when killing things like the alarm clock and messaging programs.
Again, the browser is ONLY running when it is in the foreground, i.e. you are actually browsing. If you are on a site streaming a video or audio, then the browser will keep running in the background. Otherwise its NOT running. ANd again, killing apps causes the phone to use MORE battery, not less.