Have you tried writing an essay while talking to someone else and ended up writing something wrong and incoherent and had to go back and rewrite some parts? I have.
Our brain works best with one thing at a time. When your mind is working on more than one thing, it is like that other person trying to speak and grab your attention, and it ends up decreasing your performance in the primary task.
Organizers were invented for this purpose - to clear things out of your mind, so you focus on one thing at a time, without fear of missing things. I'd say as long as you have a system to achieve this, you're good. You don't necessarily have to have an actual organizer. However, to make this system work, you must make sure that you 1) use it, and 2) trust in it.
You should come up with an organizer system that you have faith in prompting you to do "the right thing" at the right time, and frees up your mind any other time. For example, I put post-its on my desk, my laptop, or shoes to remind myself what I need to do when I get to these locations. I use alarms to remind me of my appointments or scheduled tasks.
Whatever system you chose, you must trust in it. Once you start using it, don't worry about it not working. Just use the system, and forget about the task until your system prompts you at the right time/place. This will ensure you spend your valuable brainpower for the task at hand.