Yes, the paint should be removed. No, do not seal the slab prior to tiling.
I answered a similiar email yesterday so I will print a portion of it. Others may have different stripper suggestions which is fine so long as the chemical is nuetralized after it is has been used.
Actually it is recommended that any paint on a concrete slab be removed first. However, it is recommended that chemicals NOT be used to do this if possible as there may be an adverse reaction between the chemical stripper and the thinset mortar.
Most thinset mortar manufacturers recommend that the painted surface be sanded and wire brushed to scarify and remove the paint residue. Sometimes all the elbow grease in the world will not get the paint off the concrete and a chemical stripper is needed.
Here is a heavy duty paint stripper that should work real well should you need it.
It s the last product listed. CSR, Inc. is located just about everywhere. If you use this product follow the directions to the teeth and rinse well afterwards with plain water. Then mix a cup of laundry detergent to about 3 gallons of water and scrub the slab clean with a scub brush. This will help to remove and neutralize any remaining chemicals. Rinse with clean water and allow a day or two for slab to dry before tiling.