It depends how they are connected. If its through and ignition controlled relay then no. If its hard wored from battery to battery then in theory yes.
You will need to keep them seperate as not to flatten the start battery over night.
The tug battery will not charge your house battery it will only equalise between the two.
So if your using current in the van with car connected it could take the tug battery below starting voltage.
I hope this helps.
Kezngaz.

Hi.
Put a battery in van with regulator and panel\s to suit on roof of.
then either a second battery in car with dual (electronic) isolator to such. and wiring through Anderson plug to van wiring.
That way you have two power supplies, to van. One when disconnected. and no fear of draining starter battery.

A panel on roof of car helps too,
If you have fridge/freezer in rear of car .

There are lots of systems. check and do the one to suit you and your wallet.
Just an isolator and one spare battery will do the job. Basically.

Car charges battery during day
. Battery runs lights/tv in van. fridge if compressor.
car recharges next day. Fine if you basic and travelling every day.
a lot did/do that for yrs.
A panel on roof will take charge past equalisation of redarc.
An "electronic" switcher WILL take battery further up the charging scale.
Read up on it and have fun.

You need much higher voltage ( pressure ) to charge . Unless you have a DC to DC charger ? You need the alternator runing to charge second battery ., Make sure the cables are big enough to prevent voltage drop !!

Standard set up is that the alternator charges the van battery (so only when running) and the car battery is given priority charging by an isolator under the bonnet. I don't think the car battery can be flattened by the van battery when you are stopped. If in doubt, unplug the appropriate plug.