Unless you're going to be getting a lot of heavy traffic on these stairs (like dragging things up and down them), you should be fine without putting a nose on them. As long as the tile is set and grouted properly these aren't going to go anywhere.
Just to give an idea of the longevity and wear resistance, there's a house near where I live that was built in the early 20s with a similar type of tiling on the front stairs, and based on the other architectural elements appear to be from the original construction. Most of the places where you can tell that tiles have replaced in the past are at the bottoms of the risers, not the nose. If you're worried about losing a tile here and there, just store the extras from the installation somewhere in case you have to make repairs.
That said, a more important consideration would be traction. This type of tile can get really slick when it's wet and even worse when it has snow on it. It is much more common to use a complementary stone surface on the treads and mosaic on the risers to give better footing and make them easier to clear snow and ice from.