I've had that happen twice so far.
(former fleet mgr for way too many Ford E-series) The E-series powerjoke used to do what we called a "run-in" where the EGR valve would hang get fouled up and hang on a hot-soak start up, and it would continue to crank AND misfire until the engine caught and ran. What would be a 1 second crank could be as long as 5 or 10 (if it was really hung and still started), or not start at all. It felt exactly like that, where the engine would fire on a cyl and the starter would continue to crank and intermittently fire, until the engine ran-in over the course of 5 or 7 seconds. Ran rough as hell for a couple of seconds and then smoothed right back out.
I honestly had flashbacks to that happening, but then I remembered that I wasn't at work, I wasn't in a diesel, it wasn't hot out and this was MY CAR. I called my local dealership that minute, and they said they had no recorded events of it there, but that if it did it again - bring it in. I've even taken to shooting video of the startups in the morning hoping to catch it in action.
Mine didn't at ALL feel like a low-battery issue, as I definitively proved a month prior that the OEM battery had a bad cell in it, and got it replaced under warranty.