The engines and the aircraft existed, due to the technological agreement between Nazi germany and Japan. Japanese Metallurgist weren't too smart, this is why they couldn't create a turbojet engine on their own that was decent enough so the German engineers from BMW and Heinkel sent over blueprints and several models of the BMW 003 turbojet and many german aircraft designs, and the Japanese engineers at Nakajima and Ishikawajima basically copied the design but it was so advanced that they had to replace sometimes entire components that could meet with Japanese manafacturing capabilities and science at the time.
In short.
Yes, though no aircraft is ever known to have been built using Pulsejets.
And here is a nice artwork:
German engineers knew that pulsejets were very inneficient at fuel comsumption and created a loud humming noise and also didn't produce as much thrust, especially on takeoff hence the 2 small Rato Units. This is why the germans didn't even bother to test pulsejets on it.