This related to, but not a duplicate of Are Martian winds as strong as portrayed in "The Martian"? Answers there show that because the pressure is so low on Mars, even a high wind velocity doesn't result in that much force. You would feel a windstorm on mars, but it wouldn't be enough to knock you down or blow a rocket over. So, from a wind perspective it's unlikely a launch window would be delayed.
Dust on the other hand may be a bit more of a problem. Dust storms on Mars can get pretty high, up to 40 mi/60km in the atmosphere. At ground level the dust isn't likely to be that much of a problem, at 20km up a launch vehicle would be going at a very high rate of speed, so dust particles could damage the leading surface.
However dust isn't likely to stop a launch. Mars dust storms can last for weeks, even months, so designers would have to build a solution into any spacecraft that would need to return to orbit or meet a launch window back to Earth.