yes and no. Most exoplanet detections so far have been indirect: people just search for the dimming from the eclipse or similar other methods. So you're right about that.
But recently we're starting to actually directly take sensitive enough images to be able to see planets (see http://planetimager.org). They aren't using NNs yet. But there have been discussions of using NNs for various aspects of those searches.
Detecting dimming is actually surprisingly difficult and currently partly done by humans using Mechanical Turk-like platform. https://www.planethunters.org/
Dude, stars don't have constant brigthness...
Might be kind of overkill. The patterns being looked at for exoplanets are periodical dimming of stars AFAIK. I don't think you necessarily need a neural network to sift through that.