If you’re going to learn how to write them either way, you might as well start now. Certainly it will help you memorize them better. Is it the most efficient way to memorize them? Maybe not, but you don’t have to be efficient. You should enjoy learning Japanese however you like.
If you write down every kanji during reviews I think you will eventually become overburdened, even with the amount of time you have available to you. I think later on you will also want to start focusing on grammar more. But you can always adjust your learning routine based on your priorities.