I think there is potential for this to be a small blessing in disguise. I think Brady has been zeroing on Welker a little too much in the last few years, and I think it has led to less efficiency when they get down in the red zone. He used to thrive by spreading the ball around to whoever was open, and the offense also used to rely more on the running game. This injury may force them to go back a little, and use more double TE sets, run the ball more, and spread the ball around a little more. This will make them a little less predictable, and possibly a little harder to defend.
They will obviously really miss Welker on those 3rd downs, when Brady wants someone he can really count on to get open and catch the ball...but hopefully they can make up for it by looking for other guys.
Really though, Welker is relatively irrelevant to this teams championship aspirations. Their offense is not what it was 2 years ago, and was never going to carry them. This team is going as far as their defense takes them. So unless they show that they can defend good offenses, and make big plays, they don't stand a chance anyways.
But I am an optimist, and have seen enough from this defense over the last few weeks to think they are hitting their stride (last game notwithstanding). The secondary has looked much better with Springs stepping up, and Bodden playing excellent, and with Sanders coming out of nowhere to add some more pop next to Meriweather. And even the pass rush has looked decent, now that they are mixing it up a bit more with stunts. I certainly wouldn't put money on this team, but I would not be surprised at all if their defense (and a classic Norv Turner playoff performance) bring them to the Superbowl.