In general I would say yes. These are making a re-appearance as "survival tools" or 3-in-1 Axe that you can pick up cheap Chinese versions for a couple dollars at a flea market.
However there are some older "Antique" varieties that were made with quality metal and were probably quite useful. I am guessing that your may be of this variety although it looks to have led a very hard life.
The nail puller is broken off the top and looking at the 3rd picture it looks like this was one with wooden handles that are now missing. See the one here for reference purposes.
Vintage Old Collectible Swordfish Hammer Hatchet Nail Puller Tool | eBay
You might want to get a couple shots of the makers mark there and find some old tool forums and see what they can tell you about it. I'm no expert just an internet commando but that doesn't strike me as the Flea Market variety and it just may be worth something to the right tool collector.