It is a trial to get the sausage cooked if you put it on raw. My wife's preference is to put it on raw, so I make sure it's right on top, the last thing I put on. I think it cooks quicker that way.
But, most times I'm using traditional Aussie beef BBQ sausages.
If beef is a little rare, not even the missus gets excited.
When I do have pork sausages, I lean towards a little pre-cooking.
I just throw the chunks of sausage on my turning peel and lay it on the coals for a minute.
Works for caramelising onions, too.