Dropout implies stochastic descent? The question is very simple, yet I can't find a quick confirmation on the web. It might seem obvious - by design, will Dropout always result in stochastic-looking gradient descent? (SGD) 

I've built a system which converges nicely with momentum at 0 and learning rate 0.01, even with 100 layers stacked. With dropout, the error decreases, but jumps up and down due to dropout knocking-out certain neurons?

Is it usual to see fluctuations of error during backprop with dropout, similar to SGD?

Would that  imply I can train on huge batches instead of minibatches, without the fear of overfitting by default?
For example, using Resilient Propagation (rProp) - in my test-example the LSTM trains in just 40 iterations using rProp, instead of 1000 using SGD
It depends a bit on your definition, usually the stochastic part of Stochastic Gradient Descent refers to the fact that you sample mini batches and estimate the true gradient with this sample. Dropout adds stochastic behaviour by sampling masks that comes down to sampling new network architectures every time. You could certainly see this as a form of stochastic gradient descent but whether this is the case or not depends solely on the definition.