Yes it will rebloom off of old canes. Think of the old canes as a camels hump. They store water and nutrients that the plant will use during it's dry winter rest period. If those old canes weren't there the plant might die during the dry rest period as it has no reserves to draw from. If you don't give it a dry, cool rest in winter it won't bloom.
Thanks for this, the old canes seem so battered,bless them. There are a few dry stumps in the pot so I don't know what happened there...Perhaps I should think about repotting after it has flowered...Or should I leave well alone???