I do not have the covers on many of my biowheel filters - for I have the tanks on the bottom of double stands and to pour water into the filter to prime it after a water change is nearly impossible - and I hate futzing around with the stupid lids back in the back when I do it!
There is no problem with dust. Dust is a part of life. It is fine. The only reason you might want to watch a bit carefully is that sometimes the wheel can toss droplets of water up and out of the top of the filter. When mine do that, the droplets inevitably land on my lights. I do not like mixing electricity and water.... so when that happens I make sure I keep the lid on.
Turning biowheels are very tempting to a kitten. I have had one delivered to me in bed at 2am by an over-acheiving hunter. Great - he managed to "kill" a biowheel....
I know that the biowheel, being in a place with loads of water and oxygen available to it, does hold a nice colony of beneficial bacteria. I keep them in the filter and working for me as much as I can.