Yes. All the way around means outside flanges, inside flanges, outside web, inside web, and flange toes.... i.e., continuous weld on the inside profile of the channel and continuous weld on the outside profile of the channel.
On first glance I agree with Scott.
BUT, since we can't see and don't know the joint configuration, the weld type, or any other of several variables it may be a bit premature to just say 'YES'. It would really be nice to have a picture or sketch of the exact welding symbol. At least more description to help us 'see' what you have.
He Is In Control, Have a Great Day, Brent