Jisho

見 inside of this word is nothing, just a character that is being used to write a word. Depending on the word, you can often still assign a word-specific meaning to single kanji characters inside them and assign them a reading, but that's about it. You wouldn't say that something is a noun or a verb or an adjective etc.

For 見学, it's clear that 見 is being used with the reading けん and roughly with a meaning of just "seeing", as in physically looking at an object. (Not with the meaning of "opinion" or "hope / outlook (on life etc.)".) But whether you think of that meaning in your native language with a verb or with a noun is not relevant.

And some words even that is not possible. Consider 煙草. While meanings are clear, we cannot make a statement about readings now. Or 出鱈目. Now readings are possible to assign, but the meanings have nothing to do with the meaning of the word.

All that really matters here is that 見学 is a noun (which can be used as verb with suru), there's no real way to assign grammatical roles to the component parts, but if you find it helps you to remember the word by assigning roles to it, go ahead, just be aware no one else will know what you mean. Best you can analyse the word by looking at the kanji is that it's "something to do with seeing and something to do with learning", in this case it happens to mean something like "learn by seeing", but you wouldn't know that unless you know it. Compare it to another word like 見事 which means something like "something worth seeing" but again, you only know that if you know.

In English, "fly" is a verb. So in the word "butterfly", is "fly" a verb or a noun? As flayxis-san explained, it's nothing. It's just part of a word. It makes no sense to break a word in half and ask about the grammatical category of one half.

But "fly" is also a noun (the insect). A passage from online etymology dictionary quotes: "butterfly (n.)
common name of any lepidopterous insect active in daylight, Old English buttorfleoge, evidently butter (n.) + fly (n.), ... Perhaps ... simply because the pale yellow color of many species' wings suggests the color of butter."

"+ fly (n.)" ==> evidently linguists do take interest in what each part means, whether it was a verb or noun individually.

In case of Japanese, IT MUST HAVE A CATEGORY. Because otherwise, there's no rules to whether you would say 見学 or 学見, 青空 or 空青 and everything would be chaos. Precisely because each parts has a category, its meaning and pronunciation may change depending on the way it appears in a compound.

For "blue sky", you must say 青空, and the second kanji must be a noun (it can be an adjective "empty" in or words 空白, but not in this case), because in japanese and also chinese grammar, the main noun must comes last in a compound word and everything that describes it comes in front.

I agree that for beginner, you shouldn't be thinking about this issue. But that doesn't mean you should tell them that there's no rules whatsoever, or just make up rules that are wrong.