Hello Kim!!! Sure it can!!! Let it just callous over by letting it just lay in a dry spot in the shade for a few days and then try to plant it in soil. I put a piece in soil that was hardly 6" and it's rooted. Why not try even if you don't succeed? If you do you have 2 plants.
Here's some encouragement.
2 of my cuttings rotted while rooting.
I clipped ridiculously to the top.
I was about to toss these two nubs.
But I remembered someone saying "Plumerias never cease to amaze us".
So I tried what most people won't. I let them dry, then stuck them in one pot.
Put them way in the back of my "I don't need much attention" plants (where the sun shines in the morning, and the sprinkler hits it in the evening.
Several months later...
Now they have their own pot... ~_~
B/c I've actually done it, I can say that it is possible to root tiny cuttings. I don't recommend making cuttings this small on purpose. However, if you catch yourself in a situation like mine, you can try rooting, knowing there's a chance for it to survive...
So, yeah...make two plants from your broken one.