The issue is the output rating (power) of the Outboard’s Alternator
It’s a very small output, which is sufficient to re-charge a battery after starting, but insufficient to charge a depleted house bank.
If the outboard
alternator is connected to a depleted house bank, requiring a “lot” of amp-hours to recharge, the alternator will be overloaded, causing premature failure. The house batteries will not likely be adequately recharged.
There is no particular danger
Don't ask a single
pony to pull a 4-horse wagon.
BTW: Many small outboards don't even have a regulated charger
, suitable for battery charging
; but actually have an un-regulated power supply, only suitable for running lights & etc.
Welcome aboard GB, and hope this helps.