I think it's hard to know on Morneau, but I would guess no trade.
If the Twins manage to sign a pitcher like Dempster or Marcum to shore up the rotation further, add an additional vet for the back end/insurance, suddenly the rotation looks solid with Marcum/Dempster, Diamond, Worley, Gibson, Hendriks/De Vries/Walters/Waldrop/FA #2. It's one thing to go in the season needing 2 guys to step up from that last pack, another to be looking for 1.
Honestly, they should still have money to look for help at 2B/SS to have insurance against Dozier/Florimon not being ready/MLB-quality AND get a quality 3B option in case Plouffe was a fluke. Carroll slides back into the utility position he's best suited for and suddenly you've got a very nice bullpen coupled with a decent rotation and a solid lineup...why not ride that team, see how they do with a healthy Justin Morneau in the middle of the lineup (and hopefully after a full healthy year, no longer bailing out on pitches from LHers). If it doesn't work, you can look at dealing him at the deadline, but that's a team you can sell to the public as worth watching.
The rotation still wouldn't be top-end, but there'd be 4 pitchers who would qualify as being reasonable #2-#3 starters. And a massive improvement over last season. Offensive drop-off is likely in CF and LF (Willingham will likely regress a little due to age), but there's potential improvement (overall) for RF, 3B and 1B. Unlikely the offense at SS & 2B can get much worse! So why couldn't the offense be better?
No need to rush Arcia at that point. Progress in 2013 is a good idea to set up 2014, from a marketing standpoint...and from a team standpoint. Isn't it better to stagger out your rookie development a little if you can?