I've been trying to decide if I'd say it was "appropriate" for an eleven year old. Ultimately, I've come to the conclusion that I can't tell you. Green Arrow comics are a little different than most, but not by a whole lot. They do tangle with some more mundane and "real" issues than most (for instance, his current sidekick has a sorted past, and there is detail about it in some books). However, I think it'd be up to the individual child.
Here's what I'd suggest.. Stay away from the Mike Grell issues (they're excellent, but definitely not very child-appropriate). Judd Winick, who is currently writing the "Green Arrow and Black Canary" title is a much different author though. I'd suggest that you head over to a bigger book store that carries graphic novels and look for some of his Trade Paperbacks.. then read some for yourself. I know that both Borders and Barnes and Noble carry them, so that might be the best way to see if you, yourself approve of them. The Trade Paperbacks are basically just collections of past comics, and a good way to read an entire story.
Some writers are different than others.. so the comic's maturity will change. Meltzer's "The Archer's Quest" (Green Arrow book 3) is excellent, and I'd see no problem with giving that to an 11 year old. But some of Winick's books might be a little different.
In any case.. They do talk about Archery a fair deal in some books. It's a neat way to read about a comic character who shares your interests. I'm just a big kid when I read about it... Of course, the day I shoot my longbow as well as Ollie does.. I'll be the coolest guy in the world.