Neural networks can give an approximation of any function. The only consideration to do is the dimensionality of the search space, which give constraints to the amount of data you have to get a good approximation.
For a supervised network (you use autoencoders, then I think you use some variant of backpropagation), it's difficult for me to immagine how you think to do the trainig using single positions because you need similar positions in your training set. Maybe your approach is different, but I'm convinced that second strategy (using features) is more promising. I think using positions require a huge amount of data training to get good results.
For features take a look here, and to the classical work of Shannon.
I taked also useful informations from the source code of Crafty.
But you have to extract these informations from the FEN string.
Autoencoders are a way to give a reduction of data (good because increase performances). It seems to be better the use of Pincipal Component Analysys, as reported here.
I hope this can help you.