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Whether this will fry the alternator depends on the alternator's internal circuitry, and the boat's circuit wiring.
Typically, if the voltage sense lead (field lead) is disconnected, an alternator's regulator will say "Oh my, there's no output, I must work harder!" and immediately go to maximum output power. If there's no load attached, it will burn out in a very short time.
On newer "smarter" alternators, they are designed to protect themselves from this kind of failure, and they'll say "Oh my, I must work harder! But no harder than this" and they'll shut down if necessary to prevent overheating. How to find out? Contact whoever makes your alternator, and ask them directly.
The mixed blessing is that sometimes the protection components themselves can fail, so the smarter alternators are (brely) more expensive and arrguably less reliable since there's more stuff to fail in them. In reality...modern equipment uses regulators with what is called a "heroic" mode that protects against failures of all sorts. Boats don't always have "modern" in them though.
So you got lucky, either your boat or your alternator/regulator was smart enough to protect it from failure. In general, the rule is to never leave the alternator running while disconnected, because MOST of them will indeed burn out very quickly in that situation.
There's probably some simple way to alarm that condition, like installing an audible low oil pressure alarm on the engine. Engine is off, oil pressure is zero, alarm will ring if the power circuits to it are still active. Or, like they say in Ghostbusters, "DON'T TOUCH THAT SWITCH!" (VBG).