EA Applicant Waiting until RD deadline to file CSS?

Our son has two schools that require the CSS, both of which are reaches for him (Fordham and Ithaca’s Park School). We’ll know about Ithaca before their deadline, but Fordham’s CSS deadline for ED and EA is fast approaching. The financial aid office’s states that students who miss the deadline will be considered for RD aid. Is the amount likely to be less if we wait until we find out if he’s admitted to fill out the CSS? With a 3.1 GPA and 1320 SAT his odds of getting in aren’t great, and the amount of grant aid probably will be low (although every little bit helps).