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Premise - a team with a bad offense won't lose anything changing defense for offense.
2008 worst AL offensive teams: (runs per game) - with DER rank (in majors)
TEAM --- R/Game - DER (rank) - W% -- 2009 data
Oakland - 4.01 - .700 (4th) - .466 --- 4.23 - .689 (19th) - .431
Seattle - 4.14 - .682 (26th) - .377 -- 3.73 - .698 (12th) - .485
Royals - 4.27 - .690 (16th) - .463 -- 4.17 - .679 (28th) - .446
Toronto - 4.41 - .704 (3rd) - .531 -- 5.09 - .703 (8th) - .544
Oakland improved its offense, sacrificed defense, and got worse.
Seattle improved its defense, lost offense, and got better.
Royals see their offense and defense both go down, (as well as their winning %).
Toronto improved its offense by .6 runs a game, but only have a modest win% gain to show, (the defense was stagnant, but they slipped a bit in the defensive standings due to other teams improving).
The evidence does NOT support the notion that sacrificing defense for offense is a silver bullet for improvement. 
Honestly, I don't think most of the people screaming for offense have an actual notion of how much gain a switch is going to have.
Endy Chavez for Ichiro -- substantion offensive gain -- .665 to .853 OPS (4.0 to 7.1 RC/G).  Well, that RC27 value is based on an entire lineup of the player.  But a player is only 11% of the lineup.  So, a quick and dirty judgement of how much swapping Endy for Ichiro's twin brother would be:  3.1 (the diff in RC/G) / 9 = .34444.  Over 90 games, that would be an extra 30 or so runs.  (This is a very simplified method - and lineup position changes things a bit, but as a quick and dirty, it IS in the ballpark).
If you replace Endy with another Ichiro, the club moves up to about 4.1 runs a game, good enough for ... LAST PLACE in offense in the AL.  Who thinks Carp is going to immediately be just as good as Ichiro?  The simple truth is that you CANNOT fix an offense where 5-7 bats are under .700 by swapping in one player.  The ONLY way the Seattle offense is going to move toward average is if the 5-7 slumbering bats wake up. 
Me?  I'm all for getting Carp in the lineup.  I was a Carp fan BEFORE the trade materialized.  And I think the upside here is swapping Endy for Ichiro offensively, (though, he's a rookie, so there's a boatload of downside).  As to how many runs Junior costs in LF?  Could it be more as much as the 30 runs gained?  Yes.  Could be less.  Could be more.  But, the performance of the other 7 bats outweighs the performance of the 2 that we're talking about by more than a factor of 3.