Okay, so in case anyone ever happens to have this same odd question, here's what I learned. There do appear to be some differences inside c2runtime.js that check for cordova specifically. Most of them seem relatively minor.
But the biggest difference is that within index.html, there are a couple listeners that will suspend the game when the app moves to the background. That turns out to be essential because if you don't suspend the game when the user switches apps, iOS will most likely kill and reboot the app, losing the user's progress.
So if you ever end up in a situation where you're building a cordova app where you load in a construct game (rather than just exporting a single construct game as a cordova app), make sure you listen for cordova's pause and play events, then call cr_setSuspended accordingly.
Aaaaand this will probably help no one. But I was pleased with myself that I figured it out.