Hello,
To answer your question: Yes, the pitchers can totally fill up. Or at least untill the bugs on top can't get out. Usually when the pitcher has an excess amount of bugs above the digestive zone, or about half way up the pitcher, the plant will get "indigestion", or it will start to turn brown, and the pitcher will die. All of this is normal. Every once in a while, one of my pitchers will topple over from so many bugs, filled to the brim! Hope this helps,
Kevin