i don't know about naval combat ships, i bet they don't broadcast AIS, but i have been at sea many times and rarely recall seeing a large tanker of container ship not using it. so a naval vessel should be able to at least receive, but i don't know.
on the radar scan, a ship the size of a container vessel looks like a giant bratwurst. you could read a book by the return signal.
I retired from the Navy in 1994. I suspect the features you mention are programed into the current tactical data systems computers on our Navy ships. AIS is unknown to me, Naval vessels are exempt from Federal regulations requiring that system. However that does not me0an that may have that system installed. Know what you mean about blip size. Have seen radar returns on 300,000 ton ULCCs in the early 80s in the same waters as the McCain’s collision.