If the Http Request I am testing does not use any cookies, will using a cookie manager give better results? In Jmeter documentation using cookie manager is considered a good practice, but in this particular case it's my understanding that it shouldn't make a difference.
Well-behaved JMeter test must represent a real user using the real browser accessing the system under test with 100% accuracy, it includes:
If the application you're testing doesn't use cookies, i.e. neither sends Set-Cookie header itself nor parses Cookie headers from the incoming requests then using HTTP Cookie Manager doesn't make any sense, it will only give you some overhead.