Question: I am redoing a bathroom, converting a tub to a shower and I plan to install green-board above. The existing 1/2" drywall has some issues (flaking paint, nail pops). I'll be replacing the walls and the obvious choice would be to tear the ceiling out and replace it too.

But ***because there is loose cellulose insulation above the ceiling***, I'm considering just applying a second layer of drywall (using long screws) on top of the current ceiling.

I'll be adding a vent fan, and I'm prepared to cut through two layers for that. I'm also changing overhead lighting so I'll probably use box extenders.

I've seen double drywall done for fire protection, so I know it's possible. Is it a bad idea in this situation? What problems might I encounter?

Answer: 
I don’t see any problem, with multiple changes I believe it is a better way to go. Even using an electric blower to move cellulose when I pulled it down there was still a mess. The others we did were overlays.

In a bathroom is 1 place I suggest using hot mud or setting compound for those new to Sheetrock. Hot mud is affected less by moisture than standard mud. Get the 1 hour stuff not the 15 minute and when it starts to set, toss anything that's left in the pan and mix a new batch.
i see no problems other than the new fan may have some tabs that fold out to install it above the drywall and with 2 layers, they may not work right. add some blocking and prepare to drill your own install holes in the metal housing of the fan........Maybe :)