I did have both voice and data roaming enabled. So I don't know if it would have worked without. Actually - I do. They disabled my voice roaming when I didn't pay a roaming bill (it was extortioate, I was disputing it) but my texts kept coming through.
So I would disable voice roaming if I were you. The charges to answer those spam calls are ludicrous. Just one or two second call to identify it's spam and hang up - 10-20HKD. Disgusting. I will be checking alternatives to Birdie at some point because of this.