You mis-understood!

Think you mis-understood what the LZ said. 冲销 probably means crediting to or replacing work study or you don't need to do work study.  Under this condition, merit-based scholarship helps.  But it depends on the school.  The richer the school, the more likely it helps but only to some extend.  If merit-based scholarship exceeds the amount of work study, etc. then financial aid is reduced no matter what school.