Feasibility is in the eyes of the beholder...wait did that sound right??
Anyway, Festus2 was quick to the draw in steering you the right direction before I could even finish typing the first reply. That's great people at work for ya
If that is what fits your needs, sounds like a great way to do it. Anytime you don't have to drill into the side of your TT, you have just made future possible issues disappear! Many people have not felt comfortable with a heat source as close as a side mount grill would be, to the side of their TT. Your solution would be great. Just keep an eye on that gas line supplying your BBQ. Don't allow it to be in a location for innocent bystanders to walk on, or damage and you'll do just fine.
Post some pics of your endeavor, when you have the chance ! I'd be interested to check it out!