Only if the terms is in the staging contract you signed with the stagier. Also, what constitute a success sale should have been spelled out - do you consider successful if you sell (for the full list price? for 90% of the list price? just sold and nothing to do with the sale price? The time frame? sold within a month? 3 months? 6 months?)
If they want to charge a success fee, there had better be a definition of success if you ask me.
But bottom line is , what does your staging contract say? If it does not say that, I won't worry about it, if it does and your situation fits, then you probably have to pay.