As I said below, my data indicate a slightly lower rate of error in procrastinated papers than otherwise. It'd be a bit of a leap to conclude without more research that procrastination helps. But lets say it did turn out that waiting to the last minute resulted in writing with fewer errors. What might the reasons be?
Usually when students explain that they prefer to procrastinate, they allude to creative energy of some kind that only arrives as the deadline looms. I can't recall a student ever telling me they made less errors that way, but such a situation isn't entirely unimaginable. In my imagination, the student thrives on the stress of needing to put a paper together in a short amount of time and actually becomes more productive. Although this is possible, I'm fairly skeptical. Sometimes I've thought I became productive when I procrastinated and then found a bunch of performance errors circled by my professors.
Students who struggle more with cognitive errors (a term I'm not in love with) may be a different matter. Since they misunderstand the rules of grammar, they can actually make their papers more error-filled the more they work at them. But since my study was of freshman composition classes and not basic writers, this seems unlikely to be the main explanation.
Maybe fewer errors isn't even a good thing. People screw up when they push the boundaries of their comfort zone. Freshman papers often contain errors that simply come from imitating a style they haven't yet mastered. Helping students to master the style they're already going for is a lot easier than trying to get students to stop writing sentences that sound like they could follow "See Spot run." Students who think that grammatical errors are what separates good and bad writing may have perfect grammar but still write bad papers.
I need to go back to the papers that were procrastinated on and determine what kinds of errors they contain and whether the lower rate of error might have been caused by playing it safe and not attempting anything more complex than a compound subject.