I'm planning a similar forge myself. I'm surprised no one has chimed in yet. I'm new to this stuff so take my advice for what it's worth. I don't think the gas burner would get hot enough to benefit you much except maybe getting your coal/charcoal burning. I would think that the high heat of a forge would burn out the burner pretty quick.
I'm planning on putting a pipe along the bottom of my old grill with holes in it for an air supply. Then line the grill with clay to insulate leaving the holes in the pipe exposed to allow air to flow in. Then just get an air supply (hair dryer, mattress pump, etc..)and load it up with your fuel source. You can control the heat some with the air flow.
Do a search here and you can probably find some good info. on converting the grill to a forge. I know there was one on here not long ago about making one out of an old air tank that might give you some good ideas.
Aaron