Does inverting a sub effectively make the enclosure bigger?

You are likely overestimating the space gained by inverting the sub and underestimating the physical footprint of the magnet and voice coil assembly inside the baffle itself. While it's true that the motor structure moves out of the cabinet, that space is occupied anyway. The magnet is massive, and the physical volume it takes up inside that 15 inch footprint is still significant. Assuming it gives you a substantial volume increase over the actual internal displacement is a bit of a stretch. At 1.5 cubic feet, that is certainly pushing the limit for sealed operation on a 15 inch driver. You won't be dealing with a lot of headroom or easy tuning, which is normal for a space this constrained. But if it is a sealed design, it will run. It's a very small volume, so the driver will be operating at a high air velocity, and you'll want to ensure the enclosure is perfectly sealed and that the sub is rated for those internal pressures. If you are running something like a high-excursion driver, you need to make sure that the sub is actually rated for the low excursion volumes you are running.

My experience has shown that when you put a large driver in a tight space, the primary issue isn't ussually the cubic feet of air, it's the structural integrity of the whole setup. Those thin MDF boards will vibrate themselves apart long before the sub chokes. You need significant bracing inside that enclosure, and seriously, put dampening material in the surrounding body panels, not just the well itself. Otherwise, you're just building a glorified speaker for the car interior and it will sound like it is rattling itself into pieces.

So yes, you can seal it up, but don't think it's a huge victory. You're going to be managing vibrations more than you're managing airflow, and that is a completely separate project.

One thing I'd test before the glue dries is wether the well itself is actually airtight, because on most cars that recess has drain holes, wiring grommets, or spot weld seams in the floor, and if any of that leaks you're not really at 1.5 cubes anyway, you're at an undefined number that changes with how well the tape sticks to rusty metal. I had a similar setup years ago and slow-pressed the cone by hand with an amp off, and it hissed right back up thru a seam I never woud have found by eye. Also double check your polarity flip against the actual wiring at the amp, not just the terminals, since an inverted mount is easy but a reversed signal somewhere else in the chain is a genuinely annoying thing to trace.

Gotta push back on the air velocity thing in the first reply. A sealed box doesn't really have airflow issues like a ported one does, the air just acts like a spring. There's no port chuffing or anything to worry about, so I wouldn't lose sleep over that part. What actually bit me on a similar small sealed setup years back was power handling. Small volume means the cone stiffens up fast and you lose output low, so people crank the gain to compensate and cook the coil. Just feed it sane power and it'll be fine. Did you measure the well with filler bags or are you eyeballing that 1.5 figure?

Update: so I pulled the board back out and went over the well like the leak comment suggested, and sure enought there's a wiring grommet in the floor that was never sealing anything. Got that plugged with some silicone. Still stuck on whether the inverted mount actually buys me usable space or if I'm chasing pennies. Would you just measure the driver displacement and call it done?