Hey, Jenn, you found the right spot. Pic upright below for those who were also seeing it sideways.

Yes, you can cut it, yes the cut-off part can be propagated, yes the stump should sprout a new top. It looks like there's enough material there to make several new plants, depending on size of each. Does reading this discussion give you the info you need? 'piercing my ceiling'. Scheffs, Dracs, Ficus, all very similar in pruning/propagation, except for the stuff about Scheffs and Ficus making side branches/'filling out,' doesn't apply to Dracs.

There's also timing to consider. When did you have in mind for doing this?

Cutting it back is probably best left until Spring (at least conventional wisdom suggests that).

Thanks for the advice. I hadn't thought of when to cut it since I wasn't sure if it was even possible--I don't want to kill it! I just want to get rid of the brown growth and maybe start a new plant or two.

Yep, cut in March, should sprout but might take a good four weeks to do anything!

I'd wait until June so that the plant has gained some energy back after the winter indoors. If you can get it outside in some shade, that'll really help re-vitalize it. Then, when you chop, the new growth will resume that much sooner.

Josh