I imagine it depends on what you are applying for. If it's DCP, then no resume is needed. I'm pretty sure that a computer program reads those applications, so a resume will go unnoticed. If it's for a PI, I have no idea. I don't personally know anyone that has applied for one.
But, I do know many who have applied, and been accepted into DCP. None of them attached a resume to their application. You get to put yourself forward when you do the phone interview.