For most, no.... they just want you to be able to be licensed. So, if it took you more than 7 years... or more than 3 tries... you need to focus your fellowship apps on states which have more lenient requirements. I'm assuming this is not the case for you, though. 🙂
For the highly competitive ones... it can. So can your OKAPs. But that's the exception, not the rule. I seem to remember seeing OKAP scores on maybe one or two apps... NYEE? It's been a few years.
As far as I know, reference letters is the real crucial thing... especially your chairman/program's director's opinion.