There's nothing to suggest that's even remotely true. Super Bowl championship teams almost always win because they improved from within, not because they made some big splash in free agency -- and certainly not early in free agency, when guys are getting overpaid left and right.
In fact, of the past seven Super Bowl champions, NONE of them signed a free agent within the first 10 days of free agency who made any real impact whatsoever.
The 2007 Giants (who went 8-8 and lost in the first round in the previous season) didn't sign ANY free agents until March 27, and the biggest free agent they signed all offseason was Kawika Mitchell -- for less than $1 million per season.
The 2006 Colts signed exactly one unrestricted free agent all offseason (Adam Vinatieri), and that happened 11 days into free agency.
The 2005 Steelers, 2004 Patriots and 2003 Patriots didn't sign a single starter during free agency.
The 2002 Buccaneers didn't sign anyone significant until March 22 -- three weeks into free agency (and that was Michael Pittman, who has never even rushed for 1,000 yards).
The 2001 Patriots didn't sign anyone significant until March 16 -- two weeks into free agency (when they got Mike Vrabel).
The last Super Bowl champion who had signed any signficant free agent within the first 10 days of free agency was the 2000 Ravens, who signed Shannon Sharpe on the fifth day of free agency.