It's possible. 

First, is there really a legal separation agreement? This is a specific legal thing. In my practice I've only seen one a couple of times. And I've been around for a lot of years.

Is the "alimony" court ordered?

Do some research on what constitutes alimony under the Internal Revenue Code.

As I learned today, there is no such thing as a legal separation in NJ. FWIW.