Denis, I can't help you with direct experience regarding dust and asthma but it a potential problem is that there is wood dust created that is under 1 micron. This is the real nasty stuff because it gets down inside the lungs and stays there. The larger stuff is either trapped by the nasal cavities or exhaled. Also, a 1 micron bag doesn't catch every 1 micron particle especially since the pressure on the bag from the inside is trying to drive particles through.
Here is a site that you might find of interest. It seems to be considered by some woodworkers as somewhat of an authority on home dust collection.