From my experience, you should at least know how kanji is written in general. Knowing each part will change the way you see kanji. If you are in the beginning stages still, I would recommend trying out multiple resources.

What are you currently using and what level are you on?

Depends on what you want to learn. If you want to learn how to write in Japanese, you have to learn how to write kanji. Learning the readings is how I think they are taught in school. I personally am just learning what kanji are used in what way in specific sentences, and what they mean. That way you can eventually write that sentence in hiragana or in kanji.

I would say learning to write is important. Stroke order is standardized and because of that (and just culture in general), there are specific normal ways people take shortcuts when writing quickly. Knowing how to write makes these intuitive and makes reading handwritten and stylized kanji easier.