I'd say to be pragmatic, you should learn it to an extent, but not to the degree that a University will force upon you.
Chinese characters are composed of radicals. There are relatively few radicals, compared to the sheer number of composite characters. And that makes sense, from a mathematical point of view. You have radicals x, y, and z, now how many permutations can you create from them?
So the question is, should you memorize those permutations, or just the components? I contend: just the components.
I assume your goal is to be fluent in the language, be able to read and write in a meaningful way, and to handle yourself in any situation in a Chinese speaking country. If it's calligrapy, sorry, better get memorizin'. I know Chinese who have been honing that fine skill for decades.
The point of learning the radicals is pragmatic: to be able to look up words in a dictionary quickly. And when you're learning a language in any way that's not electronic, you'll be doing that. For example, you're on the street reading a menu for tea. You saw an appetizing character. Well, the fastest way to look up what that is to write it in a character-recognizing dictionary using Google's Pinyin input or Pleco on your phone.
And to write that character and have the software actually recognize what you're scribbling, you should help it out by learning to write those radicals in the proper stroke order. Then, a few swipes of the finger, and done.
I used the Tuttle Beginning Chinese Character (or whatever it's called) book, which contained a few hundred characters and by proxy I learned all the radicals I ever needed.
Producing characters from memory, by hand, is useless. I live in Taiwan and have never, ever had to write a character by hand. I also know Taiwanese expatriates who have since forgotten how to write a large number of characters from memory, but this does not hinder their ability to read. Recall and recognition are different things, and although the ability to recall does aid in recognition (http://mobile.nytimes.com/2014/06/03/science/whats-lost-as-handwriting-fades.html?_r=0） I cannot say from experience that the effort required to do this for Chinese is worth the benefit.
I remember the characters I've looked up just fine. The reason I believe I'm successful at it is because I'm conscious about analyzing a character for its radicals at the moment that I look it up. The first time I looked up ma 嗎 I thought, huh, that's a horsey-looking picture on the right, and a little box on the left. And the dictionary says it's a grammatical particle.
Later on when I looked up ya 呀, I thought, that's a toothy-looking picture on the right, and a little box on the left. And it's a grammatical particle. And then I looked up ba 吧. A bun-looking character on the right, and a little box on the left. And hey, it's a grammatical particle.
At that point my brain said, "You know what? I think that little box on the left, that I see every time I look up a grammatical particle, probably means, grammatical particle."
And because you were conscious about seeing a character's forest for its trees, your brain formed patterns. You'll get better at deriving the meaning or pronunciations of new characters because your brain formed patterns about those radicals. Life will be swell. New characters will be a treat.
But memorizing every picture by rote just so you can never use the skill in a real-life situation? No, thanks.