But would 1406 cause a drivability issue? My experience with egr's is that the only monkey with idle.
Depends. The DTC is because the measured EGR flow is not as expected. Usually this means not enough EGR flow. But it could mean too much EGR.
Bottom line is, too little EGR flow will NOT affect drivability. It will cause a "check engine".
Too much EGR will affect drivability. How much depends on the conditions at the time (idle/power/how much excessive flow there is).
If the EGR flow is way out of wack, it could create all kinds of problems such as what you are experiencing. However, for it to be that far out of wack, one would expect the EGR valve to be rotted out to the point where it is flowing all the time (not likely here).
As I stated in the post, the DTC may be false itself (DPFE). If so, then the DTC has nothing to do with your base complaint.
It could just be a smoke screen to your real problem. At the very least, the DTC would prevent your car from passing inspection.
I would be real surprised if changing the cats made the P1406 problem go away.
I am normally a test first and then replace kind of guy. For this problem, I have changed out more "good" parts in the interest of narrowing down the real cause. Can be frustrating.
Good luck.
PS, if the DTC code had been in the original post, I would have chimed in much sooner.