I don't think there is a "right" answer to that question, it's something you'll have to judge for yourself if it's worth your time. I can try to give some information on what you could expect the knowledge of radicals could give you, in order to help you make a decision.

The most obvious reason to learn radicals would be to be able to use a kanji dictionary, though this is probably not as useful as it used to be, since other ways of looking up digitally have become possible. However there is another fairly useful reason to know the radicals, and that is to be able to guess either the meaning of a character, or the way to write a character that you're trying to remember.

To give an example 棋 碁 基 all these characters have 其 in common. If you're not familiar with radicals, then you have to separate them by rote memorization. On the other hand, if you are familiar with them, you can use their meaning to make a logical choice. 将棋 (shogi) is a chess-like game where you use wooden pieces thus 木. In 囲碁 (igo also known as simply go) however, the pieces do resemble pebbles rather than wooden ones (and quite possible were in the past) thus 石. 基 refers to foundations and fundamentals like 基本　基準　基礎 and is thus 土.

This was just one example, but you can often make the same judgements on other characters as long as you know which part of the character is the radical, which isn't always obvious. A lot of the time it is to the left (棋), but it's also common that it is on top (花 艹 most of the time refers to plants and flowers), or like in two of the examples, at the bottom (碁 基), but they can also appear on the right (戟 fairly rare character meaning halberd, radical is 戈 whose meaning is very similar), or in other places if enclosures are being involved.

Now all of this knowledge is not completely limited to people who specifically learn radicals, as I'm sure you already knew some of the things i wrote, or could logically come to the same conclusions without any specialized studying. But I think making an active mental effort to learn does help somewhat when trying to remember a characters or trying to decide which of the characters is the most likely to be correct.

I should add that I do not think it should be your main focus, but something you do on the side to help you solidify your knowledge as you go along.

This post turned out longer than I expected, but I hope you found it of some interest, and made you able to form your own opinion of it is something you think is worth learning.

It really depends on what you mean by "studying radicals".  "Radical" is a confusing term that's used for several different things depending on the book you look at.  If you mean 部首 (the single component of a kanji that it gets indexed under in a dictionary), then RTK does not teach you that and it's probably not important to go out of your way to learn it.  If you're talking about a looser definition of primitives or components, it still depends a bit on what exactly you mean by "studying" them.