Can a 800 fps air rifle kill a small hog?

It depends on the size of the hog, The size of the caliber, the weight of the pellet and if you can get in a good head shot.

Assuming you are using a .177 caliber rifle. (your stretching the limits of the rifle)

I would select a H&N Baracuda Match .177 Cal 10.65 grain pellet.

Don't get hug up on speed. A heavy pellet will fly slower than a lightweight pellet but will fly straighter and have more knock down power than a lightweight pellet.

Hopefully your going after really small hogs, because I think you are stretching the limits of you rifle if it's a .177 caliber air rifle. I recommend a larger caliber, but it's up to you.