In my experience, as long as its healthy, yes! It will not grow directly from the cut/broken top directly, but from the nodes (the junctions of existing leafs and branches and the trunk).

It kind of looks like you have new growth emerging from a few existing nodes, but its hard to tell from the picture.

Good luck,
-daniel

Yes - it will back-bud. How vigorously it will back-bud is directly related to how much stored energy the plant has at the time of the injury (right now most houseplants should be just past peak energy retention [stored food]), the time of year, and how much light and air circulation the plant gets subsequent to the injury. It's not a big deal at all, so don't be too concerned - all will be well.

Al

Thanks for your encouraging words!
Daniel, there is no new growth buds at all, you're probably talking about the little pointy pieces that are at each stem.