If there's enough smoke to cause concern, he's probably not using shielding gas. Its very common to have hoses to suck away smoke from flux-core and stick welding, can see why a down draft table would have worse effect. But I don't think a vacuum cleaner is gonna draw enough air volume do do much across a 2'x3' surface.
The hoses I'm talking about have maybe 10" diameter funnel opening on the end, and you just lay the funnel opening near the weld site. Seems like you could do that very easily with your vacuum cleaner- just run the vacuum cleaner hose into a hole in the bottom of a bucket, and sit the open bucket mouth near your weld.
My grandma had one of those Rainbow vacums, was pretty nice, but spendy. I've always wanted to try modding a wet-dry shop vac with an internal pipe from the hose inlet that ran down to within .5" of the bottom of the dust bin, then putting a few inches of water in. Seems like it would give the same effect, for much less cost.
