There are phantom draws on the battery that will eventually drain it to nothing after 12 - 14 days but seeing that you are plugged in to 120 shore power, I see no need to turn switch to off.
It would be a good idea to keep an eye on the battery once a week for a few weeks to make sure the onboard converter is doing its function properly. Also invest in a multi tester/voltmeter. HF carries them for around $4. For maximum battery life do not draw down below 60% S.O.C. or 12.2v before recharging. I have a pair of group size 24 Interstate deep cycle 12v that are just over 10 years old and still functioning very well. I depend on them a lot as I usually boondock. No solar or generator used either.