The f:stop is equal to the focal length of the lens divided by the physical size of the aperture. If you add a 2x converter, you are doubling the focal length of the lens but the physical size of the aperture stays the same, so your 50/1.8 lens becomes a 100/3.6 lens. Plug the numbers into a DOF table and see what you get.
Doublers also usually add some transmissive light loss--often around 1/2 stop. You don't notice it if you are metering through the lens, but if you use a handheld meter or non-TTL auto flash, you might want to test it, so that you can take it into account.