Yes and no.
The first and most important point is that you SHOULD NEVER have an open flame near saw-dust if it's just been kicked up into the air in a cloud. If you haven't done the experiment where you light a cloud of flour on fire in chemistry class, I'm sure you can find the video on youtube. The same thing happens with sawdust: it will explode. This is going to be ESPECIALLY problematic if your garage has poor ventilation, because you'll be trapping the excess propane along with the airborne wood particles.
So if you're going to brew in your garage, make sure that you don't do it RIGHT after you build a table or something.
If there's only a LITTLE saw-dust in the air, then you run into the same problem that you would in any brewing situation: airborne particulates carry bacteria and wild-yeast, and as they settle into your brewing kettle you risk infection. That said, as long as there's not too much saw-dust floating in the air, you shouldn't have a substantially greater risk of infection than you would anywhere else.
Aside from wild-yeast and bacteria, there's nothing inherently bad about having some wood in your beer. Some beers are intentionally conditioned with oak chips. Your sawdust should, after a week or two, settle to the bottom, so you shouldn't get any in the glass.
There's also nothing wrong with sawdust on the floor (as long as it isn't getting kicked up into the air.) Some breweries keep sawdust on the floor intentionally, in order to sop up spills - although I think sand, or a good floor grate is more common.
Good luck, and let us know how it turns out!