The offense wouldn't be better off, but the team as a whole could be if they were able to then focus the cap room they would save on Welker into the defensive side of the ball.
The Patriots have been a top offense for the last decade, so its not going to change because of 1 player. Production would go down from Welker's position, but the offense as a whole could still perform at a high level if they found a replacement for him and made up for his production with a few receivers, like Edelman and Hernandez.
I wouldn't pay him more than $8 million a year, even though he deserves more than that. Paying Calvin Johnson money on a WR better get you a Calvin Johnson and that isn't what Welker is. Hes the best slot receiver in the game and fits well into this offense, but if you plugged someone else in there, they could get 80-90 receptions in his place. Yes, that is a dropoff in production, but the drop off doesn't go from 110+ catches to 0 catches...
The defense needs a "shut down" corner badly. When Talib went out with that injury, Boldin had a field day against the D, making plays all over the field and outjumping and outfighting DBs for the ball. Guys like Talib can reduce the number of times that happens and really free up the defense from a scheme perspective.
It kills me to say it and it will kill me to see it happen, but because of what Welker will demand in FA makes him a player that they can no longer afford to keep on the roster. Just remember what happened to the Colts with Marvin Harrison, he was around Welker's age when he wanted his final big payday, and he ended up costing them big time on their salary cap as he aged to 34 or 35 years old and retired... They were hurting bad from that contract, because his production fell off as he aged and didn't match what he was making per year.