I think the US armed tugboat in SH3 is a placeholder for several different classes of tugs.
The USN (and RN) had a lot of ocean going tugs, generally just over 1000 tons and armed with a 3 inch gun plus some light AA. Wikipedia mentions that USS Navajo's depth charges went off as she sank and I would guess that implies they also had sonar. They sometimes sailed with convoys and were especially useful during beach landing operations, for example HMS Warspite was saved by a couple of large US Navy tugs at Salerno.
Take a look here
https://en.wikipedia.org/wiki/Cherokee-class_tugboat or here
https://en.wikipedia.org/wiki/Abnaki-class_tugboat
Am I missing something?
edit - I've just found a 1943 USN tug called the "Gay Head". Be careful when googling that one...