Is there a way in a saved search to reference a formula from another column in the same search?

only if you incorporate the same formula into the other formula

This column does a case when statement and returns a 0 or 1. I have another column that wants to reference that 0 or 1 without having to re-write the formula again

nope, unfortunately NS doesn't support / offer this

Depending upon the complexity of the 1/0 statement you could put it into its own record field. Sometimes repeating the formula gets too big or too complex