Your Cummins ECM looks for a minimum eng RPM before it will allow the injection system to work and fire the eng. So it's very possible that tired batteries will slow down how fast it starts. However, the other thing that can cause this is weak and leaking injectors. If that's the case then it will get worse and you'll generally notice it's using a lot more fuel.
But keep in mind that the ECM has to see acceptable inputs form all the eng sensors before it will start. So if the eng stops in a particular spot it may need to trun a bit more to get all those readings.
Nine years is good for OEM batteries, I would replace them no matter what. Better to do it now than be left sitting someplace.
Good luck,
Scott