Would a ducted fan with a nozzle like a jet engine have more thrust than a normal ducted fan?
but why not use the pressure created by the fan and contract the space making the output velocity higher?


That is exactly how the pressure energy added by the fan is converted into thrust. Thrust, after all, is the product of the speed increase between free stream and exit flow, mass flow and nozzle area.

That real jet engines don't show so much contraction is due to the expansion of the core gas flow from heating. If you don't add heat, your exit area should be quite a bit smaller than the entry area.

If by "normal ducted fan" you mean one where the duct is simply a cylinder of constant diameter, then yes, a properly designed nozzle will create more thrust.