Radicals: inescapable?
I feel like this question could elicit subjective and open-ended answers, but here goes anyway ...

In Beijing, one of the classes I had was a dedicated 汉字 (Hànzì, Chinese character) class. In it, we were learning the most common radicals, and some word examples that contain that radical. We learnt how, often, the meaning is conveyed by the radical and the other portion is often a pronunciation component. I found this to be enormously helpful; even without recognising some characters, I could sort of guess at their general meaning and, with the context of the sentence, understand what was going on.

Contrasting this to the general classes I attend at 孔子学院 (Kǒngzǐ Xuéyuàn, Confucius Institute) where they do not teach you any radicals, simply tell you to learn and remember the new words yourself, I notice most classmates struggling to remember "which little bit goes next to the bigger bit." I found my prior knowledge of some radicals helped me learn the characters quicker than my classmates, and my belief that they are of importance continues to allow me to learn previously-unknown-to-me radicals and characters faster as well.

They are important. They are necessary to learn. However, whether you specifically set out to learn them first, or if you gradually learn them and get a feel for them as you continue your education ... that part is up to you.

I, for one, would definitely recommend to keep them in mind, but not necessarily learn 214 common ones before learning any whole characters. I would probably learn a character, figure out what the radical stands for, see if there are other variants (like 心 xīn: heart radical has a couple of different forms) maybe look up a few other characters with that radical, then press on with the next character in your book. Rinse and repeat.

Note, there will be certain characters where the radical doesn't appear to provide any understanding of what the character means. That's just how it goes sometimes: you might think it's stupid and it should have [x] radical instead of the [y] radical that it has, but you could say the same of any language really: some bits are just nonsensical, and you just have to remember it but not necessarily understand it (the best lesson my calculus teacher ever taught me: "You don't have to understand it, you just have to know it." took me from a C to an A.)