The White Sox signed Konerko to 5 year $60 million deal that is a great PR move for the club. Whether it will turn out to be a great baseball move is yet to be determined.
Konerko will turn 30 in March, so the Sox will have him for his age 30 through 34 seasons. According to Baseball Reference, players similar to Konerko through age 29 include Kent Hrbek, Jason Thompson, Fred McGriff, the Big Klu, Bobby Thomson, Carlos Delgado, Jack Clark, Lee May.
The comps aren't bad as some players did extremely well after age 29. The one thing you do notice is that the OPS+ of most of the players do decline sharply by age 34. The notable exceptions are Jack Clark who had an OPS+ of 167 at age 34 and Carlos Delgado who just put up a 161 OPS+ at age 33.
The five year average OPS+ of each player listed:
J. Thompson: 102 (2 years; done at age 31)
McGriff: 122 (and solid seasons after age 34)
Kluzewski: 114 (tailed off quickly in after age 31 season)
B. Thomson: 92 (had solid age 34 year with Cubs, OPS+ 116)
Delgado: 151 (4 years through age 33 season)
May: 113 (league average by age 34)
Paulie has had an OPS+ over 120 four of the last five seasons. His comps suggest that he can very well continue to produce these types of numbers over the next couple of years. It's more likely than not he will have a noticeable decline in his numbers by the end of his contract. But some players have continued to produce well after age 34. And we also need to keep in mind that many of these comps are from eras where players had radically different lifestyles and training habits (meaning they felt like I do at age 32).