Even if leaving one open doesn't set any codes, it'll still mess things up fuel ratio wise. The point of egr is to recycle unburnt fumes in the exhaust and raise intake temperatures to reduce kr (also chemical components of exhaust gas reduces kr slightly). So now the computer will be adjusting the fuel ratio for the expected exhaust gas and getting fresh air instead. Now, it won't cause a terrible difference since exhaust gas is mostly air, but the worst problem is that the air it's pulling in is not filtered!!!
While setting the code isn't the best case, it tells the computer to adjust the fuel ratio as if the egr is defective, so it would be better to do that and deal with the code rather than inject the wrong dirty air to mask it f that makes sense.
