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No, You can not paint wood with emulsion as it wont give smooth finish, first of all paint wont stick to the wood surface. Emulsions are plastic paints, usually mixed with water to paint. Best option would be to use Enamel Paint for the Wood or better use Wood Polish.
Subsequently, one may also ask, can I use wall paint on wood?
Wall paints are designed to work for walls. Painting on a wooden surface is not a good choice of material. The furniture can be painted using wall paints, however, there is no guarantee about the durability of the paint. Wood Primer is a general purpose oil-based primer for interior and exterior wooden surfaces.
Keeping this in view, can you paint furniture with emulsion paint?
For stools, chairs, tables and shelves wait for a week before use. If you can't face the bother of eggshell or gloss, you can get a good and surprisingly hard-wearing finish using emulsion paint. Clean and prime as above then paint using emulsion. Apply two or three coats.
For flat panel doors might be cheaper to just get new depending how you value your time. Painting woodwork with matt emulsion is a terrible idea. It won't last and won't clean easily. It's designed for walls.