Pretty much, plus a couple of extra steps. I've been looking online for pictures, but haven't seen any yet, so a verbal description will have to do.
First, make a rivet block for your vise. This is just two pieces of steel with a hole the size of your wire drilled between the meeting faces so it holds your wire securely. The easiest way to do this is to glue the blocks together with a sheet of paper in between, then drill the hole, then soak the paper off.
Next, grip your wire in the blocks with a bit sticking out and gently form the dome.
If you want it smooth and shiny, you'll need to make a rivet set, just a punch with a polished hollow in the end. Hammer the rough dome, then put the set on it and hammer that down snug. It may take a while to get the feel for how much wire to use.
If you were using smaller wire there's another method in which you hold the tip of the wire vertically downward in the tip of a torch flame until it starts to melt. It will form a ball, at which point you immediately quench it or it'll fall off. Then you cut that off with enough wire to make the length you want the rivet to be, slip it into a hole in a chunk of steel, and hammer it into a domed shape, followed by the set if you want. That's how I do my countersunk sterling silver nails I use to fasten silver inlays to hawk handles. There's a pictorial on that around here somewhere, but I can't seem to find it.
Edit: Found it! https://www.bladesmithsforum.com/index.php?/topic/37778-this-is-why-im-always-recommending-files-to-people/page/2
about halfway down the page.
That's 18-ga wire, it may work on 16.