Yes but the fan you mentioned will be running on 12 v directly, and wont be going thru the inverter, but will still contribute to the overnight drain on the batteries. And the other items you have, assuming they are all 120v appliances, (regular house current) then they will run thru the inverter.
As mentioned by others here, if you buy the 12 v versions of the items in question, you might not need an inverter, but even tho many of us have converted most of our mobile electronics to 12v, there are still a few items that you might have or want to buy in the future that will need an inverter.
Common items that might need an inverter are cordless tool chargers, small kitchen appliances, cpap machines, electric razors, laptop chargers, etc. Many or all of these can be bought in 12 v versions but assuming you have some of these and want to keep using them, you will need an inverter to do so.
Also as mentioned, an inverter will draw a small amount from your batteries when it is turned on, even if nothing is plugged into it, so its always best to turn it off when not using it.
Finally, as far as overnight loads, yes, you should be OK, but what are your plans for recharging? You cant just keep pulling small amounts for many nights and then expect to have fully charged batteries forever. You will need to recharge the batteries, preferably daily.
The three ways most of us accomplish that is either with a solar panel array, or driving the vehicle with provisions to charge the house batteries, and third, hookup to a generator or shore power.
