No, it is not possible at this time.
Live Editor does not use simple text files like the main MATLAB editor does: a .mlx file is a zip'd directory containing a number of items including XML files.
MATLAB Function Blocks do not reference .m files. It is not simply a header block together with the name of a .m to invoke, so it is not a simple matter of changing to parsing to permit referencing .mlx files as well.
Instead, MATLAB Function Blocks store the code as one of the properties of the block, inside a XML file, with .slx files turning out to be a zip'd directory containing (mostly) XML files. The Simulink block structure itself would have to be altered to permit Live Editor code.
... This should not be interpreted as "It is not going to happen": this should be understood as "It has not happened as yet, and there are complications that make it tricky to implement, so it might take a while."
