I am in the yes camp of this. My opinion is what difference is the flying base to a normal base? You would base and flock etc a normal base so why not a flying base? There's no difference between the two besides the stem. Now, you do not paint the stem, that remains clear. Painting that would look stupid.
The arguments for not painting it was so you can see underneath it. Well you cannot see under normal bases can you, so what difference does it make? Sure you can land on top of ruins, but who would want to do that besides to drop troops off?
People even say if you base the flying bases then the bases will not match the board. Well here is a news flash, if you base your models they will not match every board anyway!
I just think basing the flying base is no different to any normal base and if you do not base it then they will stand out like a sore thumb and look extremely odd. Plus you are odd for not basing the flying base :P
Here is a based flying base, I'll mention that I do mine like this, though this one isn't mine:
As you can see it looks no diferent from a normal 60mm base except for the stem in the middle.
What is your choice people? To base or not to base?