I haven't directly trained arms in over a year and they've grown an inch ... with that being said there are other variables you have to consider when you want to grow ... ie caloric intake, diet composition, and type of routine you're doing.
With that inch I gained in my arms I also grew everywhere else and did a lot of compound movements, but that was the plan. It wasn't like I just said fuck my arms and blindly went about doing other things ... I did the research and through trial and error figured out what worked best for me to attain the goals I had set up for myself.
Could direct arm work have increased the gain I made in my arms ... maybe, maybe not. I'll tell you in a year.