Would I sing it? Can't imagine why not. I have many, many times.
It's a very mild story as these things go. No murder, no death at all; no naughty words (but some good cursing), no politics, no blackmail, no racism - nearly a children's song.   

I learned this from President Taylor in 1966. He sang the Carthy version. Being too lazy to get up and look at the LP notes, I looked at the words & notes in the Carthy unofficial website. Carthy relates it, as Mary does above, to the House Carpenter songs.

I enjoyed the mistransription at that website:

They hadn't been sailing a week or more
When her love oh it turned to anger
He bit her and he kicked her he called her horse
And he back to her John in the morning

A bit more on its history:
Roud (#907)gives a reference-only entry (no text) for Peggy and the Soldier in Wm. Thackeray's broadside list (c1689)

Malcolm - I don't find a reference in G~D (though I often miss them). I see a ref to The Gallant soldier - Roud #5792. It's sometimes called (elsewhere) Peggy and the Soldier but seems to be a completely different song.

Roud lists the item Carthy (as you say) seems to be referencing - the text in Journal of the Folk-Song Society in 1930. That, says Roud, is from Dorset : Lackington (they also reprint a text in the Skene MS of mid 1600's.) Roud also gives a different English field reference to Peggy Went up the Street from a manuscript collection of Cecil Sharp, Folk Words p.256.

Anyway, it's a fine song.   It goes right in there with my list of trad songs involving "Truly Pissed Off People." All of a sudden at the end, Husband comes up from being a wipped wimp (see ROCKING THE CRADLE) to the strong character of the piece. You just wouldn't want to risk sailing on any boat builded by the man that builded Soldier's boat - or on any waters on which it might have sailed.