I understand that the On- and Kun- readings are important to know and understand. However, what about the Nanori readings? Are they worth studying if I am aiming to just take the JLPT tests?
No, you definitely don't need to know nanori readings for the JLPT. Honestly, you can read a lot of basic things pretty well without knowing very many nanori readings.
Why? Well, suppose you see this (derived from Japanese Wikipedia):
You may have no idea how to pronounce 安倍晋三, but as long as you recognize that it is a name, you'll survive. For example, later on, you might read this:
For all you know, maybe 安倍 is pronounced ばびうべぼ, but for the purpose of understanding the text, you know that the 安倍 here refers to the same thing as the 安倍 earlier.
Now, of course, if you know that あべしんぞう was the prime minister of Japan, but don't know that 安倍晋三 is read あべしんぞう, you'll run into problems down the line. Eventually, you absolutely should learn as much nanori as you can, because they are useful to know for reading names in real life (though, even if you do know your nanori, reading Japanese names in kanji can be fraught with peril).
But for basic texts, including the JLPT (in which all passages are pretty much self-contained), nanori are a low priority.
Also, as a practical matter, it's not really effective to sit down and "learn all the nanori readings" in the same way that works for kun and on readings. If you look at Wiktionary's list of nanori for 一, you will see that there's a lot of them - 13, by my count. But even if you memorized them all, you probably wouldn't be able to read the name 一彦 correctly on your first try (let's assume that you know that 彦 is pronounced ひこ in names).
It turns out that 一彦 can be pronounced いちひこ・いつひこ or かずひこ・かつひこ (I think that いちひこ and かずひこ are more common than the other two), but not いひこ or おさむひこ or すすむひこ or はじめひこ or ひひこ. (Of course, the other nanori are used in other names containing 一.)
Over time, you'll probably get a feel for which combinations are likely as names, and which aren't (for example, I intuited that いちひこ and かずひこ were the only correct readings, which was close - there are also the two other variants I listed) - but sitting down and learning all the nanori for kanji isn't going to get you there.