MLP and backpropagation limitations?
No.  There seem to be multiple misconceptions here.

First, linear regression.  Linear regression assumes that the errors are normally distributed.  It doesn't require that the inputs be normally distributed, and normally they won't be.

Second, neural networks.  Neural networks certainly don't require that the inputs are normally distributed.  I'm not sure where your colleague is getting that from, but it's just not true.

Yes, neural networks work fine in higher dimensions.