Is my understanding of a gas turbine engine compressor correct?
..the rotors add dynamic pressure to the airflow..
  
  ..this dynamic pressure airflow is transformed into static pressure in the stator vanes.


are both incorrect partially correct statements, but can be open to confusion. Dynamic pressure is transformed into static pressure continuously, by narrowing the passage through the compressor. The rotors add total pressure to the airflow, some of which is extra dynamic pressure and some extra static pressure.


The rotor vanes increase the energy contents of the gas stream. Another name for the energy contents of a gas stream is enthalpy.
Energy contents can be transformed into gas speed when allowed to expand (dynamic pressure) or into static pressure when you keep the volume confined. 


For ease of reference, just take a car tyre as an example. Some little rotating implements in an air pump at the gas station provide a pressurised air stream into the tyre. Stop pumping and measure the tyre pressure: what you're measuring is static pressure. The weather news talks about high pressure and low pressure systems, that is static pressure as well. It's energy contents that has not been converted into a velocity yet, like increasing potential energy of a rock by lifting it up further.

Now get a match stick and press on the tyre valve. The air streams out of the tyre, this air stream can be called dynamic pressure. You can use the outflowing air to inflate another flat tyre, you're then converting static pressure in tyre 1 into dynamic pressure into static pressure in tyre 2. End pressure in tyre 1 is lower than when you opened the valve: total energy contents of tyre 1 is now divided over 2 tyres. No energy was added, only pumps can do that, by converting electrical energy into air pressure energy.

For the axial compressor in a jet engine:
* The rotor vanes act as the air pump, and add energy into the air stream: total pressure is increased. 
* The stator vanes do nothing with the energy content of the air stream: total pressure stays the same. The swirl is removed, and some dynamic pressure is converted into static pressure.

From The Jet Engine issue 5 by Rolls Royce: notice how the total pressure rises in the rotors, and the static pressure rises as a function of the passage narrowing.