How does backpropogation behave when there is a dropout in FC layer?
Correction made (see edit log):

No, there is no need for that.

For all dropped neuron, the corresponding activations are simply zeroed out so the corresponding gradient will also be zero.

Now because you do not want to update the parameters, you simply multiply the gradients with the same dropout mask as was used in your current iteration. 

If you're using a library, you just have to do everything as it is usually done because this is already being taken care of.