This article is from the Photographic Lenses FAQ, by David Jacobson with numerous contributions by others.
A lens of focal length f and f-number N with a teleconverter of magnification K attached will behave in all respects like a lens of focal length K*f and f_number K*N.
If the aperture diameter and focus are left untouched and an ideal teleconverter is attached, the lens will focus at the same distance, the image, including the diffraction effects and lens aberration effects, will be K times as large, the exposure will need to be K^2 times longer, the hyperfocal distance will be multiplied by K and the depth of field will be divided by K. A practical teleconverter will also contribute some of its own aberrations. (See the technical notes.)
On the other hand, if you open the aperture to keep the same effective f-number and hence the same exposure time, the image will be enlarged by K, the diffraction will be unchanged, the depth of field will be divided by K^2 and the hyperfocal distance multiplied by K^2. The aberrations are increased by three effects: the lens is opened to a larger aperture, the teleconverter multiplies those (probably larger) aberrations by K, and then combines them with some of its own.
Since the focusing is unchanged, the minimum focusing distance is the same whether or not a teleconverter is attached. (See the technical notes.)