Watch out for the
6.7L shouldn't be idled for a long time or it clogs the DPF; the 5.9L cummins you have can be idled all the way to an empty tank (would take 5 days at idle) with no ill effect. Diesel engines are designed to idle and if you look at your engine hours (if you're equipped with the counter) it only increases when UNDER LOAD. There's no difference between a heavy service diesel and an automotive diesel.
As for the convertor needing air... they only need to be cooled when there's friction involved and the convertor needs to be spinning at SPEED to generate any significant amount of fluidic friction.
BTW, I was a heavy diesel mechanic for Detroit Diesel and Catterpillar egines on drilling rigs.