Yes. Please use this opportunity to electrically disconnect the batteries from each other by disconnecting the negative battery cable from one of them and get each fully charged using a charger that will desulfate your batteries. We recommend the Battery Tender and BatteryMINDER line of products, though any 'smart' charger should fit the bill. When the charge process is complete, you should see 12.7 or more volts at each battery. If you see less (anything less than, say, 12.5), recognize that your batteries have not been or are not able to any longer accept a full charge. If this is the case, please replace them before installing your replacement module to maintain your warranty coverage.
The average 6.0 user gets only about two years of life out of their batteries. Chances are good that yours are under warranty.
If you want to increase the life of your batteries moving ahead, consider picking up a 3 watt or so solar charger that you can leave on the dashboard to provide for a charging opportunity each time the sun shines.
Also, go ahead and check your FICM's wiring harness for any chafffing as this rubbing has been known to cause electrical shorts to ground. You'll obviously want to correct any issues noted before re-installing your freshly repaired module. Page six of the guide at Dealerconnection.com lists some of the more common chaffing locations.