I installed a kitchen sink on top of the counter top. It has a flat rim and the faucet is separate (no holes in the sink). It probably should have been mounted underneath, but does it matter?
If the sink has a flat rim and you caulk it to the counter top, it should be fine. Plumbing contractors will often run a beak of caulk just under the edge and then fill the sink with water until it dries so the weight of the water will set the sink firmly in place with the silicone.
As long as the rim of the sink sits flat on the counter top and has a finished edge, it should work well. If you need kitchen plumbing help from a Tacoma plumber or anywhere across the country, Roto-Rooter can help. Call us at 1-800-GET-ROTO (1-800-438-7686) for Tacoma plumbing assistance. Tacoma plumbers are more than willing and able to assist you with all your plumbing needs.