If you can find one straight enough, I bet they'd make pretty good arrow shafts. When I was a kid (9-12 years old) I made my very first bows and arrows from sycamore, because our house was surrounded by 8 18-24" diameter sycamores. Boy, you talk about primitive.
Now them was as primitive.
I wish I had kept one, I'd post it.
I used to break branches off the tree by hand, and take one of mom's steak knives and saw knocks into both ends and there was my bow. Arrows came off the trees too. Of course, I had no clue about straightening shafts, I just broke off the straightest green twigs I could find, took that ol steakknife and sawed a groove into one end and fired away. I never shot one over 50 yards, but believe it or not, them danged little crooked twigs flew pretty straight! And I didn't even put any fletching on back then.
We still got about half of them old sycamores but they're going fast cause the older dad gets the more he can't stand the big old broad leaves that they are the first in the fall to start dropping and the last in the spring to get. I plan on making a sycamore bow here sometime soon and I would love to try some sycamore arrows out myself. Of course, mine would be from branches and not shoots, but I'd try either one. I say go for it!