Is it always safe to use WITH SCHEMABINDING in a UDF?

SO I have been reading about WITH SCHEMABINDING and how it can improve the performance of queries using a scalar UDF by omitting the table spool operator from the execution plan. I think I understand halloween protection.

My question is: If I add WITH SCHEMABINDING to a UDF used in a SP is it possible that a SP does not give the same results? If yes in what scenario?