Mounting a driver in the bottom of an enlcosure okay?

Definitive answer? No, it's going to be a compromise when you go against the physics and driver design considerations (no unit is better downfiring). That being said, if it's a dual coil with only 68 gr. moving mass and an Xmax of 4 mm then you're likely to have better results than most woofers. The sag will take longer to happen and will not be as extreme but the reason I pointed you to the google search is that this is a diy site and I was trying to stimulate a bit of the diy part. You should be fine. Now can you shows us a quick sketch of what you are doing and show us why you can't make the bottom of the box, the side? ie: rotate the cabinet.
 
Yeh here, the circle is where the driver would go but theres not enough room and the reason why I didn't want to rotate it is because the strongest side is at the bottom where the panel sits on top of the others. the box measures 400mm cubed which is 46l, the breath hole is 98mm diameter ID and is 300mm long.

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Acoustically the bottom of the enclosure is fine, but a heavy cone will indeed sag eventually.

A bigger problem is that your port
a) looks too close to the cabinet panel to be able to flow properly
b) is backing up directly onto the cone, which will be pumping air right at the port and also interfering with airflow.
c) 4" is generally too small for a 12"-check the airspeed if your box simulator will do it, otherwise I'd go at least 5." Yes, ofttimes the "ideal" ported designs just aren't physically buildable.

So yeah, redesign time.

And DON'T put elbows or kinks in the port! C'mon guys, it's common sense that will not flow air well unless tremendously oversized (and probably not even then).
 
Just some comments on what has already been mentioned.

Four inch tubing is not too small for any 12" inch sub driver I've come across and the air doesn't actually flow anyhow, it's a tuned resonator.

Yes, you can use bends in the vents, just calculate the length using the center of the tube.

Slot ports have to be calculated a bit differently than tube ports, as there can be more laminar resistance, especially if you use a radical aspect ratio. They are however, a good way to go in a tight space.
:D

Best Regards,
TerryO
 
...the air doesn't actually flow anyhow, it's a tuned resonator.

Of COURSE the air flows! It flows back and forth through the port. At high SPL the JBL guys found it acts like a big plug or cork of air, moving back and forth through the port at high speed. I think you mean it is not flowing ever-outward like an AC duct or car exhaust or such, which is correct. But it DOES flow, so the flow dynamics of the vent have to be considered, such as the laminar resistance you mentioned.

Yes, you can use bends in the vents

Well, sure, but again common sense says that will impede the airflow in the port-exactly what you want to avoid! Yes, IF the port has a big diameter and IF the bend has a gentle radius, it could work OK. Or if you never turn the volume loud, ha ha ha.
But idiocy like shelf ports bent at a hard 90 degrees at the back of the box with no radiusing is why I "JUST SAY NO" ;)