Current Marshall full time student who got in off the wait-list last year. I know it is really painful waiting so I thought I'd share what my experience was to give some perspective.
I was wait-listed from R1 with no interview. I had excellent GMAT's, no grades but graduated with honors in Math and History (UCSC from before they issued), non-traditional background career switcher, older than average.
I got an interview the last week of May, and was admitted the last week of June.
I sent 2 replies in regards to the wait-list, one after I was notified to let them know I was still interested and give a update on a career achievement, one after R3 to let them know I was still very interested.
People literally do get admitted right up until orientation, however, I think chances might be better if you applied earlier.