There's going to be a growing overlap between the two. I studied a bit[1] with one of the big SLAM research groups in the UK, and even several years ago, they were trying to combine SLAM and neural nets in various ways. A lot of their PhD students went on to ride the crest of the "deep learning" wave, and made a lot of money.
[1] Only an undergrad project a few years ago; I didn't do anything especially cool there.
I think it's likely SLAM is one of those things (like Motion Planning) that will continue to be done with more formally well understood algorithms, but indeed will be integrated with Deep Learning for feature extraction/scene understanding/many other things.
I work in the intersection of these, though primarily from SLAM background. The overlap between these communities has been increasing in the past two years.
While I think this is great, I also see that a lot of people working in the field try to take Deep Learning as a 'one-stop' approach to solving SLAM. This is worrying. Any particular methodology, if embraced without understanding pros/cons, can lead to stagnation and local maxima. It was CRFs before that, and Factor Graphs, Particle Filters, or EKF Slam before that.
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