Bill will completely ruin the atmosphere. This is a thinking man's (or woman's) game, having someone constantly making crude sex jokes and ridiculous puns will not enhance what should be a deep, intellectually rewarding experience. Besides which there isn't that much analysis when he's going to be solving increasingly complex puzzles, unless you want them to blather uselessly while Sean does all the thinking (as usual).
There are times for comedians, and times when there shouldn't be. Day 9 does amazingly on his own especially for these games (he's a pretty funny guy too but he understands when its appropriate; but Bill is 'always on')