Yep, that's how I installed mine with the mast up, one at a time climbing up as I went. However, it's not quite like building a ladder to a tree house, it was a crazy lot of work!
First of all, for each step you need to measure and mark where you want the next step. I made basically a stick with the mounting end of a step attached to the top so I could set it up on the step below and then mark through the holes. That worked fairly well most places. I thought this was so cleaver, and would keep me with nice, even steps. It did, but unfortunately the first two where off by a few inches (since they where staggered side to side, it was hard to tell) and I did not notice this until I was half way done and took a step back. Each side is evenly spaced, but the two sides are just a little out of alignment.
Then you have to drill the holes, tap them, coat the screws with something to insulate the dis-similar metals, and the screw the step to the mast. This was not bad for the first few, they went quick while I had two feet on the deck. I installed my steps staggered, so I would not need as many. This meant while working on the next step, I was standing on one foot only, holding onto the mast, using a drill, and tap, screwdriver, bottle of goo, screws and mast step parts all while trying to insure I did not drop anything.
I did use a harness, and ran a second line around the mast in a small loop from my harness so I could lean back a little on that, but still, standing on one foot, holding on and switching tools without dropping anything was quite a challenge. I found I could only do 1 or two steps at a time before needing to come down for a break, and I typically only made a few trips up a day. (I'm a fairly young and somewhat in-shape guy, but it still whooped me good) We installed them here and there while out on a 3 week trip, which was kind of fun, working on the mast in various anchorages.
For anyone else wanting to install steps in this manor, I would say go for it, just be prepared for it to be quite a bit more work then you originally assume. If I installed them with the mast down, the whole process would have taken a small fraction of the time (but cost a lot more, since the mast is not coming down for anything else for a while)