Yes, that is how the plant is usually propagated, I think. Here is an example from a position in the sun (may not be your exact plant but in the general range) where you can see the effects of very strong light (the bronzing, the compact growth) and what a clump looks like after it has a year or two to proceed. I am planning to separate those offsets in the fall. I like to wait until they start to grow their own root systems, so they are fully independent upon separation.

The branch at the base of your Echeveria nodulosa came at the perfect time. You can behead that plant (the main stem, that is) and the basal branch will grow strong in its absence. If that plant was mine I'd make the cut at ground level, through the main stem only, and allow the baby to replace the mother, and then repeat. Nature has done you a favor. It should be relatively easy to root a full-sized rosette.
Now if you're really intent on multiplying this plant, you can start by cutting near the end of the long stem and leave the rest to branch. When you force branches like that, they tend to sprout right below the rosette, fairly high on the stem, after beheading. You can wait until they're a little bigger than your current baby and then behead them to start new plants.