The offensive pieces are mostly in place, if Welker is back:
QB - Brady, Mallett (I could see this position opening up due to a Mallett trade)
RB - Ridley, Vereen, Demps, Bolden
TE - Gronk, Hernandez, Fells, Ballard
OL - Solder, Cannon, Mankins, Connolly, Wendel, Zusevics, McDonald
WR - Lloyd, Welker
It really only leaves needs at OT (not sure if starter or backup), backup OG/C, and WR4, WR1/WR3, possible WR5, possible rb (depending upon how Demps is viewed by the team)
Looking at players currently on the roster, some of the "needs" could be filled by lower end players that were on the team this year, such as Woodhead at RB and Edelman at WR4/WR5
Looking at it that way, I'm with you.
Re-sign Welker
Re-sign Woodhead
Re-sign Edelman
Draft WR in round 1 or trade up in round 2 and draft WR then
Just doing that fills every available slot except
backup IOL
starter, or backup OT (depending on how Cannon/Zusevics are viewed)
5th WR, if desired (5th being a number, not necessarily a ranking)
and makes every other signing just a camp competition, rather than a need filler.