At the level of a Tioga, you do not have a whole house inverter. Most likely the inverter powers a single circuit for entertainment items that may be used going down the road. Note that the circuit on the inverter will always use the inverter, even when plugged in.
Whole-house inverter/chargers (often 2000 to 4000 watts) and high amperage alternators to power them, with high capacity battery packs to back them up, appear on diesel pushers and sometimes large high-end gas motorhomes, rather than on entry-level C's. There are a few models of small motorhomes built as all-electric (Roadtrek's ETrek for example) but for a Tioga to have a whole house system someone would have had to install it aftermarket.
If you are considering a use that needs whole house power from batteries, this will involve replacing the existing AC/DC converter with a high output inverter-charger, rewiring the AC panel to feed most circuits from the inverter (maybe everything except air conditioning), and finding a place to put at least four large golf-cart batteries. You might also check whether your chassis has an option for a second alternator, or a higher output full duty cycle alternator; an option like this is usually available for the emergency vehicle package on van cutaway chassis, but does not come as part of the RV package used for C motorhomes.
Whatever you do to beef up the 12 volt side, it is still likely that you will need to be plugged in, or running your generator, to use air conditioning. There is just not enough power available from a 12 volt system readily carried on a C to run A/C; the ETrek does it by using an eletric-vehicle size battery pack and falling back on an engine-powered auto-start generator.
Tom Test
Itasca Spirit 29B