The obvious answer to the question of whether the Twins need to sign Joe Mauer before the season starts is yes. The shorter and correct answer is no.
Joe Mauer is in a position to decide whether he wants to finish his career in Minnesota. He will still be in that position once the season starts. He will still be in that position once the season is over. In short, it is really up to him to decide if and when he signs. It may make Twins fans and management uncomfortable, but is there really ANY advantage to Mauer in signing right now? He could have a career ending injury next year. He could be killed in a car accident. I am not sure any of us plan our lives around those kinds of possibilities. The other reason to sign is because he just wants to get it over with and not have the distraction.
On the other hand, wouldn't you want to know how much money you were leaving on the table in order to play in your home town? The only way to find that out is to go through free agency next year. No matter what other teams offer, Mauer can still decide he wants to finish his career as a Twin. If Mauer isn't signed by opening day, it isn't Twins management who is at fault. It isn't anyone who is at fault. It just means Twins fans will have to spend a little longer on needles while Joe Mauer makes up his mind.