Could you smoke a sauce? I want to add smoke flavour to a somewhat runny pepper sauce. I thought of letting it simmer on the barbeque and also have some wood chips in water to  provide lots of smoke. Keep the lid of the pot off and just put the lid of the weber on.

Can you actually impart smoke flavours to a liquid like this or would  it be better just to roast the peppers before you make the sauce?
What you're describing isn't all that different from how they make various products like Liquid Smoke (make smoke along with steam, then condense that steam).  You will need to make sure that some actual condensation occurs (for example, by having a lid for the smokey vapor to condense onto).

However, it may be simpler to add a liquid smoke-type product directly; at least the main brands are actually smoke distillates (and not artificial flavorings or similar) and thus should be effectively identical to this process, but quicker.