Hey Star,
Something is off here (.)
In any boat with a genset, a primary use case is charging up the batteries each night, or every few, while at anchor or at a mooring. Then, we come to your boat, which was marketed as a comfort yacht, and contains a metric boat load of electrical appliances. A 120VAC electric stove was standard. So, one would need to run the genset to cook each evening. A three-zone 120VAC electric air conditioning system was, if not standard, extremely common. Running it at anchor or mooring is an other major use case. Many of those boats had 120VAC ice makers. And, dual-voltage refrigerator-freezers were standard. So, even if running the refridge/freezer on 12V -- the batteries would need to be charged up.
Carver isn't now, and wasn't then, some "donkey builder." I don't believe that they designed a luxury aft-cabin yacht with, quite literally, a boat load of 120VAC appliances, huge continuous battery draws, and neglected to provide any way to use them. Keep in mind, in 1982 -- an inverter was /not/ even an option. And, even if it was -- a genset would be needed to charge up. Solar wasn't even an option, either!
Also, the 3607 was one of the top selling boat's of all time. If Carver did something this bizarre, and somehow managed to achieve such a high volume of sales, you'd be reading about it -- and the fix -- all over the Internet. Almost everyone here would know about it, why it was done, and what to do about it. A quick Google search would turn it up on owner sites as well as folklore about it. But, that isn't the case.
As for the manual, it couldn't possibly be for an earlier boat -- the 3607 was introduced in 1982! Also, the relevant parts are date stamped 10/12/1981, consistent with the boat's introduction (Sections date stamped earlier apply to all Carver's and weren't updated for this model). Having said that, it is true that what I sent you is a broiler plate manual or one from another boat (I don't know which) and might not be entirely consistent with your build. None-the-less, it is hard to imagine a specific build being as off in this way as is suggested.
As for what the prior owner(s) are telling you, I can only offer you my experience. The prior and prior-prior owners of my present boat have blessed me with tremendous background information, technical help, etc. I am eternally grateful. Having said that, that doesn't mean that everything they think they remember is correct. They are humans, too.
The International engines, PCM I think, weren't standard, but were very commonly selected option in that boat. I've been in a few examples, myself.
I suspect what the owner's manual is warning about is genset noise -- and, much more importantly, exhaust. Most of those boats were gasoline with gasoline gensets -- and gas engines produce a boat load of carbon monoxide gas. If the exhaust blows in the wrong direction, it can kill the occupants of the aft cabin -- or a nearby boat. And, Carver had a real problem with CO levels in the gasoline version of these boats. I think I remember reading that the genset could get CO levels above 3,000 ppm in some parts of the boat. I think they were just learning to understand these issues when the boats were built and it wasn't for a decade or two later that people really understood they dynamics (or lack thereof) that were causing the CO build up.
I can imagine that Carver would have gotten sued over this and added some type of safety. But, I've never heard of one. And, to my memory, by the time this issue was understood, the boats were already afloat!
Diesel gensets don't produce much CO, but do still produce a bunch of noise, foul exhaust, and a ton of CO2. So, they may not have removed the section of the manual. It is still good advice not to run the genset for a long time at the slip (although, many of us with diesel generators do it, for example, during power outages or for maintenance, when I'd hope out gasser neighbors might not, or at least might not without very careful consideration to prevailing wind, their cabins, and their neighbors' cabins).
So, viewed from the perspective of a slip vs an anchorage or relaxed mooring field (some are packed in like slips), the advice of "start it and get going" is good advice.
So, what does this mean for you? There is likely no reason that genset can't be made to run while the boat doesn't. You just need to find out why it is shutting down and address it. Without the model number and finding a controller schematic or maybe manual, I can't tell you specifically how to do that. But, I bet it involves putting a meter on a few relays to see which one is shutting things down, e.g. temp, oil pressure, AC output, external sensor of some kind.
If it isn't cooling well enough, which would be my best 0-knowledge guess, check the thru-hull, external strainer, internal strainer, hose, impeller, pump, hose, heat exchanger, hose, and exhaust. Make sure water flows abundantly with pressure to the pump. Make sure the impeller is good. Make sure bits of impeller, scale, etc, aren't clogging up the exchanger or anything else. Make sure that no hose has collapsed internally or externally to slow water flow. Etc.
Look for the usual maintenance issues. But, also, since they might be an old issue, look for a design issue, for example, is the thru-hull big enough?
