Cheeze, I doubt that the low battery would cause the engine to run slow because as soon as you start it, the alternator is giving you 14.7V. I do have to say, however, that I experienced the same thing last week with, after a week battery, the need to keep the foot on the gas to keep idle speed up. The next time I started it, later in the day, it was fine. It could be the engine computer picking up an erroneous sensor signal on start due to the low batt, I suppose.
Somewhat unrelated, I keep my engine battery charged using a charge jumper cable (cigarette lighter plugs on both ends) connected between the TV/Accy plug in the overhead and one of the dash accy plugs. Shore power cable attached to house and powered. Works great.
Q: has anyone had their coach battery relay stick ON? I can't seem to get the ON/Store light to go out. (Above mentioned cable disconnected.)