Is the comma after "Then" correct?

It's not incorrect--the use of commas is often a matter of style, and the trend in recent decades is to dispense with commas in most cases. If it is not necessary for clarity, most writers don't use them.

I have other problems with the sentence. On shipboard, the telephone from the engine room to the bridge is for general use, one wouldn't say his telephone--unless it were a cell phone, and where would a telephone cell be located at sea? Also, there is only one engineer in a ship's crew. One would say the engineer, or "someone from engineering." It's poor writing, without considering the comma.

How is it that someone in the engine room knows that there are "pirates" aboard, before anyone on deck or on the bridge knows it? That's crap writing.

Perhaps it gave the writer pause for thought as to why he didn't have the engineer splutter rather than stutter?

I would give a lot of money to see (rather than just hear) screams running past my door.

These days an engineer, to many people,, is anyone who can pick up a wrench, including those my father (an engineer) would have called mechanics or fitters.

While that is certainly true, engineer is a rating on a ship, and is either considered an officer, or is rated according to union rules (it varies from one flag to another). The other engineering ratings refer to their occupation (more or less) or occupations which once existed, such as oiler, wiper, stoker, and so forth. All in all, this passage suggests that the author does not know squat about ships.

Thanks to all of you.