Hypothetical DC electrical Question

A DP uses very little battery power once started so you likely can drive for quite a distance without the alternator. I made it from Ontario, CA to Las Vegas. You just don't want to turn on your headlights and you want to turn off all other 12V devices that you can.
As mentioned above, "if" the generator powers some source that charges your engine batteries (mine does not) you likely will be just fine but still want to try to reduce as many other 12V draws as possible as the charging source is likely not going to put out as many amps as your engine alternator would.

My rig has he ability to charge ALL batteries whether on Shore power, generator or alternator.

Now in this day and age, you can buy a unit that will automatically charge the engine to coach. It is a microprocessor that is connected between the engine and coach Via 50 to 100 amp cables. It senses which battery is above 13 Vdc and allows the transfer of voltage.
If this is an emergency, jumper cables IF your coach battery is very close to your engine battery

As already posted, it MAY work just fine.

Yes, absolutely, your converter, charger or inverter/charger will charge the HOUSE BATTERIES. On SOME COACHES, it also charges the CHASSIS BATTERIES-- by no means on all.

Some coaches have a "boost/combine" switch that closes a relay/solenoid so that the two banks are combined. May be an intermittent duty solenoid or constant duty one.

Some coaches have a low amp combiner (Xantrex Echo Charger for example), but likely not sufficient to keep up a chassis battery with loads like fans, lights, etc.

BUT, you can manually combine your banks. Whether at a battery isolator, battery boost/combiner solenoid or other place where you have large-gauge battery cables from both battery banks meeting at a common place. Merely take the large wire off one side and ADD IT to the other side. Presto, both banks being charged by your converter, charger or inverter/charger.

Amp output of the charging device needs to be considered. Said another way, a 30 amp converter is NOT the same as a 2000 watt inverter with 100 amp charging capability.

I would not take a chance that the on board systems would automatically supply charging voltage to the engine batteries. Some only do so after they sense that the house batteries are at full charge. What I have done in the past is just carry a set of jumper cables. I start the generator then jumper from the house battery plus post to the engine battery plus post. No need to jumper the negative since they share a common ground. Over the years this has gotten me home more than once.

Yes your generator/inverter/charger will become your spare alternator. No need to run it all of the time unless at night with the lights on. Don't let the voltage get too low or you many not be able to start the generator. I always thought on my Dynasty the generator was started by the house batteries. Learned the hard way it is not.

Absolutely it will work. You do need to verify that your engine batteries are getting the voltage in that situation,. Some rv's have a feature to not allow both banks together if the engine is running and the generator is running.

If the alternator is out. It still may try to disable the combining function so you would need to verify they are getting the charge. A simple jumper around the solenoid that controls that function or one car jumper cable will work but not as safely. You can either find out how to activate that solenoid mentioned or just take the wires off and bolt together or stack them up on one post if there is room. Be sure to take pictures first.

Yes if your house system charged by the generator also maintains the chassis battery with enough amps it will work.

Two summers ago I drove several hours with the ALT light on and drooping voltmeter as I knew my solar powered trailer will push some power forward to my truck. Made for a 2.5 hour lunch stop on schedule vs. pulling over or getting stuck waiting for a tow. Still everyone was booked so I did the repair in the O'Reily's parking lot in Gillette WY.

On mine the generator supplies both battery systems.
Might find a friend with a meter to verify on yours.

When I had my Triple E motorhome is was equipped with a Bi-Directional relay in the charging circuit. Which ever side had available charging voltage would send the power through the relay contacts to the other side.

All this worked very well until the day I pulled up to the ferry terminal knowing gas was cheaper on the other side. It was a wait, and I did not open the door so the head light alarm never came on. Blah, withing an hour, the chassis battery was dead. I started the generator, and blah blah, I was so low on gas, it would not stay running.

Long story was, got going and onto the ferry just in time with help from the ferry station jump start, kept the engine running for a few minutes, and all was well again.

I've read where people have actually done this to get back home. You just have to use the genset to charge the chassis battery. I'm not sure how you can safely do that though--someone with better understanding of the two systems may be able to supply the procedure.