The orientation of a speaker doesn't matter. After a few years, the spider might relax and stretch a little, maybe, but car audio subs have pretty stiff suspension to begin with, so they probably won't. Plus, underseat subs are already up-firing. I wouldn't put it right up under the deck lid though. That thing rattles.

By default, underseat subwoofers will have extremely limited xmax, purely because of the limited length of the voice coil. The entire assembly is usually around 2.5-3 inches tall, which means the speaker itself is even shorter. They're extremely shallow. And they can't usually handle tons of power without exceeding the limits of the speaker.

A more normal shallow mount sub such as the Alpine SWR-T10 will have a longer voice coil, which means the cone can more further (higher xmax) and push more air on each stroke. Since sound is transmitted through waves of air pressure, more xmax means more capability to move air, which makes more sound. An SWR-T10 has a peak-to-peak xmax of 30mm and has a mounting depth of 3.25 inches. The speaker itself is already taller than the Alpine PWE-S8 underseat sub enclosure.

Compare this to a full up subwoofer in a larger box such as the various fiberglass enclosures. An Alpine SWR-10d4 has a peak-to-peak xmax of 40mm and a mounting depth of 5.875 inches. And it has the capability to be driven beyond xmax, because Type R's typically have a peak-to-peak xmech (limit before physical contact) of about 60mm, so more than two inches of movement (note that this is not recommended, but it is possible). It also has much higher power handling capabilities than its little brother, which means more force moving the cone back and forth, which means more powerful waves of pressure, which means louder and usually cleaner sound.

There are definite tradeoffs to going with a shallow mount sub, and those are amplified when going with an underseat sub. Yes, it'll work. But not nearly as well as a full size sub would.