It's a distinction without a difference. The likelihood of a candidate "fall off" is low because companies tend to be extra aggressive in vetting candidates that apply through recruiting agencies.

My personal experience with applying through recruiters is it puts you at a disadvantage right from the get go. Most hiring managers believe applicants that come through recruiters are more likely than not to be of low quality, so right off the bat their first impression is suspicion and skepticism. On top of that, if they hire the candidate they have to pay the recruiter a percentage on top of what they pay the new hire. If you're not exceptional in every way they could possibly imagine, you're not getting the job.

Of course, there are exceptions. If a company has worked with an exceptional recruiter in the past and trusts him or her, then things are different. I have yet to meet even one recruiter that fits that description, though.