» Can a bad poker player win a major tournament?

It depends on what you classify as a "bad player".  Without a doubt, luck is a necessary part of any tournament win.  You can play perfect poker, and never make the money.  You can also play with many mistakes in your game (e.g. limping a lot, calling raises, chasing against the odds, playing a lot of hands out of position) and go on to win a tournament if you repeatedly get lucky.  In almost every tournament you will find yourself in multiple 'flipping' situations.  These near 50-50 situations have to go your way for you to advance.  There is no way to avoid many of them unless you accumulate a large stack early.

There are multiple examples of players who have won tournaments, only to never win another tournament. Jerry Yang, Jamie Gold and Chris Moneymaker are a few WSOP main event examples.  Darvin Moon freely admitted that the luck of the cards in the 2009 WSOP allowed him to never have a tough situation or be in jeopardy the entire tournament until he was heads up with Joe Cada.  In Joe Cada's situation, the 2009 WSOP Main Event winner and a respected online cash games player, anyone who watched the televised final table saw him repeatedly get lucky in situations where he was a major underdog, according to the math.

According to 2004 WSOP main event winner Grey Raymer,  "Yes, anyone can win any poker tournament; however, the amount of luck necessary for a truly weak player to win one of these major tournaments is extreme.  We're talking PowerBall extreme; millions to ONE."  And yet, there is a winner for most lotteries.  Someone must win and on any particular day, it could be you.

A deck of cards doesn't know good players from bad.  Enough of the game is decided by what's 'in the cards' that the opportunity is there for anyone to win.  As one astute player commented, "just because someone gets lucky on a hand, or in a huge pot, it doesn't neccesarily mean they are bad players."  Sometimes stack sizes and situations dictate certain moves.

The goal is to increase your chances of winning by playing optimal poker.  You want to study the game, the math, so you understand the equity value of the various situations you will encounter.  But on any given day, if the poker gods shine on you, even a bad poker player can win a major tournament.