I did two layers of newbaums over cork tape on my bullmoose bars making a multilayered grip. that didn't pose a problem. In my past life as a mechanic I sometimes double-wrapped for people. It can get a little lumpy on drop bars. That first wrap is one-layer thick in some places and overlapped to two layers thick in other places, right? When it's double wrapped, there will be some places that are only 1+1 = 2 layers thick and other spots that are 2+2 = 4 layers thick. Only you can decide if that bugs you.
The only reason I know of to do it is to make the bars a little bit bigger in your hand. There's neglible cushion there with one layer or two. The reasons not to do it would be the potential for lumpiness and the extra $10 that you spent. I re-wrap my bars whenever the mood strikes, and I buy up new colors of newbaums just for fun, so even though it's a decent investment of time, you can always take it apart and do it differently.