How much is 20 micron? Is that an easy threshold to meet?
You would need to ask someone who studies the effects of sneezing and coughing and how large the droplets become from those effects.
When working with natural processes, you usually have a range of sizes, rather than any fixed specific size. You can characterise that range of sizes (it can be a histogram and then fit a probability density distribution to it) using several different methods, e.g. by weighting according to the total number, the total volume of the droplets or the total area etc. The weighting you choose depends on the industry. One example is the "Sauter mean".
20 micron is short for 20 micrometer which is 0.02 millimeters. A 1nm nanoparticle/nanodroplet is 0.001 micrometer. Anything below 20 micron will have some affects from Brownian motion which could feasibly keep it airbourne. The effects become significant for anything less than 1 micron in size. Generally, in engineering you would calculate a "settling velocity" for your particles which, when the background air in quiet or "quiescient" (aka quite still), is the same as the terminal velocity. For very small droplets, you can assume they are solid and just do a simple calculation. Things get more complicated for larger droplets (due to internal motion and non-sphericity) and when there is motion in the background air because it can enhance/reduce the settling velocity and the prescence of the particles/droplets can also influence the motion of the background air. These processes are not well understood and poorly simulated via CFD.
With regards to coughing and sneezing, I imagine you are imparting a lot of energy to the droplets when you release them. So a lot could just end up falling to the ground anyway. Its hard to say though. There was an episode on QI where they discussed this a little bit, and someone from the audience brought in a "vomit machine" which simulated a human vomitting and where the droplets go. This is something people from that field will inevitably have studied and have a far better knowledge of.
As droplets deposit on a surface, they can either deposit all their liquid in a calm way or "spalsh", potentially releasing secondary droplets back into the air - these are called "satellite droplets". So even if you sneeze on a solid surface, it is possible you still release some droplets back towards the air.
There have been simulations where researchers have looked at how droplets move when they enter the trachea, but this is way beyond what I've studied.