Yes.

You can chop off the branch and it won't hurt your Dracaena.

Stick the cut-off in a jar of water until you see small white nubs sticking out from the bark, those will be roots starting to grow, and then plant it in a good quality medium which you can do a search here (See top of the page for the search box) and see all the debate about soils. Let the fun begin.

Oh yeah, don't wait too long after the roots start or it'll have a harder time adjusting to soil but you can just leave it in the water and grow it that way too.