While there's precedent for this, this option doesn't really make sense as the whole goal of the free upgade is to migrate as many people as possible to Windows 10 to prevent another Windows XP-like fiasco when Windows 7 hits the end of its extended support cycle on January 14, 2020.
While we can't be 100 percent certain, it seems the main point of the deadline is to add urgency. Therefore, Bott believes Microsoft will either extend the upgrade offer indefinitely, or replace it with a new free upgrade offer, but he fully acknowledges Microsoft is likely still weighing its options:
After watching Microsoft in action over the past few years, I'm fairly certain that even the top executives haven't yet decided exactly what to do in six months. That decision might not be made until very late, and it certainly won't be communicated to the public anytime soon.
If someone tries to tell you they know what will happen come that day, don't believe them.