Yes, the humanities can be saved by neuro-literary criticism, because it would give people confidence in the way that science and literature is being evaluated. Neuro-literary criticism might spark interest in the humanities, from people who are scientifically focused or who approach literature from a different way. This is a positive angle from which to approach literature.
The Humanities can be saved by "neuro-literary criticism. If everyone would keep a more open mind towards this topic then yes I do believe it may have a chance of being saved. But if everyone continues on a negative path towards this lifestyle then no it will not work out.
These attempts at pseudo-science by people who haven't taken the time to understand the fields they are dabbling in to artificially inflate their opinion of their own intelligence don't save anything. They merely make yet another subjective mass of poor assumptions and speculation that amounts to bad opinion dressed in a lab coat.
Sorry, but the failures of critical theory and the biased and largely oversimplified ideas of Marxist thought have already failed. What are they going to accomplish this time? More irrelevant criticism of scientific fields that they know nothing about? More subjective claims with little to no backing that the pseudo-intellects of the world will swarm on, like so much Deepak Chopra-like bastardizations?
We need more scientists in the humanities, vice self-agrandizing, agenda driven ideologues.
There is nothing wrong with "neuro-literary criticism," in fact it is extremely interesting and may help revitalize the humanities in the short term, the blending of psychological theory with literary criticism. However, it is just another movement within literary criticism like deconstruction or post-modernism, and will not be a long term future for the Humanities. When this fashion is over, another movement will emerge.
I do not believe the humanities are dying, they simply are not held up as much as they use to be. I think this says more about today's society than anything else. I do not believe neuro-literary criticism is going to save humanities, I do not think they are in a position to be saved.