Hard to say, give it a try and see what happens. During active times of EITMS, the factory ECM extends the pulse width of the injector to a FIXED amount over what is normally needed. It is not looking at the exhaust stream for any feedback information.
The PC already has enriched the mixture above what the ECM thinks is needed for any normal running condition. Will the net result be the combination of both systems, PLUS the extended pulse width of EITMS?... Probably so. But give it a try, because it won't hurt anything. Worst case is the front cylinder goes "slobbering rich" at idle.
On a 100* day, once the engine/primary/transmission is FULLY warmed up (just run on interstate),, EITMS should kick in within 3 minutes at idle.
Let us know what happens.
(Someone here may chime in with results because they have already tried it)
I have a power commander V, which I love, never had an issue with the eitms. Not sure if the power commander V and the III are that much different. I have it on a Road King.