You shouldn't have any problems if your battery is in good shape. The kicker does have an alternator, but doesn't throw many amps at idle. I have a house battery as well for running all electronics (radio, VHF, Finders, spotlights). I don't want to chance a dead battery at night in December! Limit the use (shouldn't use them anyway when it's cold) of livewell pumps, and other non-needed draws. Cold reduces the amperage output of your battery, as well.
Never had a problem but all I run off starting battery is f finder and running lights. I also start main motor about every hour and run at idle for about 10 minutes to charge. I also have a voltmeter on my eagle 480 ff that I keep an eye on.
Freyed: what kind of lighting did you add? I went through the trouble of putting in one light under each combing cap when I purchased my boat. After all that work I never use it. All it does is make everyone nightblind. We all use those cheap Energizer headlights from Wal-mart. They put light exactly where each person needs it. The driver does spotlight the fish with a handheld 12volt spotlight when netting like Reo. I only have the main motor to troll with, it doesn't charge below 2500RPM. After a long night of trolling the battery is nearly dead. If we shut the motor off we have to switch to the backup battery to start up again. I even have that happen during the daytime since everything runs off the same battery. That's why I have a battery switch and backup battery.