First off.. I have no experience smoking hop bines, so I can't comment from experience. I will be interested to hear your results though as I grow 9 different varieties of hops in relation to my beer brewing hobby. I will offer some thoughts on what you might expect though, especially in relation to the concept of smoking grape vines.
First thing, I wouldn't expect it to have any "hoppy" flavor. All the flavoring and bitterness in hops comes from a resin formed by the lupulin glands in the hop cone (which will have been stripped off for brewing). The resin is a very sticky fragrant yellow substance. If you chew a hop cone before the glands mature, it just tastes like green hay. If you taste it once it is mature it will be very bitter and have hop flavor. for smoking, I will be curious as to how it burns/smokes. Grape vines are a woody perennial where the vines will become woody and remain throughout the plants life (if not pruned). Hop Bines are a herbaceous perennial, where the plant dies back to the ground each year and then sprouts from a new shoot in the ground the following year. Hops are a rhizome which means they propagate in the same way grasses and most bamboo does. My hop bines get to be maybe 3/8 inch in diameter, but I do know some of the commercial outfits/varieties can produce hop bines much thicker... like 1 in or 1.25 in. So the hop bines should definitely burn different that grape vine. I wouldn't expect the bines to generate heat or a sustainable fire for cooking, like you could do with woody grape vine cuttings. I would expect it to burn relatively hot and fast and smokey....... but that white/grey smoke not the good kind..kind of like a leaf fire. which brings me to......
I imagine you'll have to dry the bines, as hop plants use huge amounts of water and I'm sure the bines will be quite wet (FYI, fresh hop cones are ~85% water by weight).
Also, if you are wondering what a bine is vs a vine. A vine grows by using tendrils, a bine grows by wrapping around a support and attaching via short hairlike structures on the stem.
Again this is all only my hypothesis based on my limited exposure to my own hop plants. I cant' wait to hear what you find out. Hope it works out.