Most grills won't appraoach the temps of a BGE or other ceramic cookers which can hit 1,000 degrees with ease. The BGE like a tandoori is made from ceramic so you have some moisture retention as well. I use a combination of the plate setter and a pizza stone so it's more indirect but not all that different from a Tandoori as I can invert the plate setter and get the stone very close to the fire. I'd say a little smoke and high temps are key to replicating a Tondoori. I've never tried it but I would suspect with a little ingenuity and some lump charcoal you could rig up a WSM to work very well.
I'd forgot how hot they get. If you already have one, it would be a waste not to tandoori with it, wouldn't it? And another argument for making the choice of a BGE, Primo, or similar if you're buying an outdoor grill.