Before you go to the dealer with mods, check all of your fittings. Too lean at idle could be a case where you are just pulling in unmetered air. You would be bleeding and running rich in boost, but that wouldn't necessarily trigger a code. Some have had issues with loose connections from the dealer.
Did you use a dashhawk to read the code? If so, have you tried to log A/F ratios?
Mazda is going to help and I will report. the stock stuff was often loose. but the hot side intercooler piping went soft and distorted. I cooled it down and replaced valve too. I have Mazdaspeed cai.. And I am sure there is more to this in ecu reading and responding.
My AFRs were a touch lean with the MS CAI @ idle. I changed to an Xcel-intake and through a cell for rich at idle. Once I put some miles on it, I stopped getting those CELs. My AFR is back to 14.7 @ idle but it creeps slowly from 14.0.
With the MS CAI, it seemed to race to 14.7 in a second just off idle.
The only difference a catted to non-catted DP will do is not let your cabin smell like raw fuel. Some owners of non-catted DPs after a few months have complained about fuel smell in the cabin... But that would be the only difference...oh, and the people driving behind you that you'd be suffocating.
I personally prefer the catted, much easier to live with and it only costs you 4-5 horsepower.