The aperture is not affected by crop factor, so the aperture of the 800 mm lens with 2× teleconverter is just ƒ/11. So the image would be darker than the lens without the teleconverter by 2 stops.

You would not have an aperture of ƒ/90. If you took an image of a particular subject with a full frame camera on the EF 800 + teleconverter combo, and then used the Raspberry Pi camera on the lens + teleconverter combo, if you tried to take an image of the same subject framed the same (i.e., same subject magnification), then you would have to move the camera 5.62 times further away from the subject. It's this distance separation that increases the depth of field of the image. If you compare the depths of fields of the two images, it would appear as if the 2nd image was taken with a ƒ/90 aperture, but only because the subject is framed identically due to the subject distance increase.

is this configuration feasible? Not in a financial sense, but will I actually be able to make out the things in my pictures? [...] Would a tripod actually let me take a not blurry photo under these conditions?

It would only be feasible with a tripod. Even then, you would need a quite sturdy tripod and appropriately strong mount in order to eliminate the possiblity of blur from most images. So I'd recommend two tripods or similar 2-point mount on the camera & lens. Not very convenient, and a huge pain in the butt to even slightly change where the camera is aimed. But anything less will be disturbed by the slightest puff of wind more than a hummingbird's wing flapping.

And of course, don't forget about surface the tripods are on. And wood floor or decking is right out. The slightest footsteps will bounce the system, causing uselessly blurred images. Even on packed dirt, the system might slightly vibrate with heavy steps within a few feet.

What would a focal length of 9024 mm look like, i.e. how far will I be able to see a human assuming a flat plane?

The table of image sensor formats and sizes at Wikipedia tells us that a 1/2.3" sensor has a height of 4.55 mm]. For regular focal lengths and longer, the following ratio holds:

(focal length) / (sensor dimension) = (subject distance) / (field of view)

So a 6' (2 m) person would fill the height of the sensor frame if they were 1600 mm * 2 m / 4.55 mm = 700 m away, roughly 7 football fields. You'd probably see atmospheric hazing and/or heat effects.