I don't know about the converse. But for an "if-then" statement, the contrapositive is logically equivalent. This statement (in if-then form) is "if you are not doing what you love, success does not matter". (I took the liberty of getting rid of the "may", so that everything is boolean, and so the law of contrapositives applies.)

The contrapositive is "If success matters, then you are doing what you love".

That... might be true. If I'm just working at a McJob, what do I care about the success of the business? I'm just there to do what they tell me, punch a clock, and cash paychecks. It pays for the parts of life that I do care about.

But if I care about the success of the business, then on some level, I love that business.