Is this sentence correct?

Yes but precious isn’t the right word to use for valuable. 
You cannot always substitute a synonym without changing the meaning of the sentence entirely. 

Do you watch the goodpigeons on the old tiny toons cartoon series. There’s a vignette  involving 3 pigeons based off the Goodfellas movie. One of the pigeons substitutes a synonym for a word and it makes no sense until he says other synonyms and then the other pigeon figures out what he’s trying to say. 

While "It is precious for young students to do volunteer work." could read correctly, it could also be as: "It is precious for young students to work as volunteers." or "Young students can do precious volunteer work."

it is incorect                     

The sentence is correct.  But nobody would say that.  Replace "precious" with an adjective that means something of substance or value.

try 

it's precious to see young students to do volunteer work.

I don't think you really mean "precious". In some contexts, "precious" is a negative word- "He was very precious about his clothing choices" means he was very picky. I have to tell you, too, that "precious" is not a word often used by male native speakers of English. I was once at a party where some Spanish speakers referred to a new baby as precious, and I realized there was something that seemed strange about it. It was men who said it, and in the US, only women would refer to a baby as "precious". Find another word. 

It's not well written.  

Young students are precious when they're doing volunteer work.

It is grammatically correct, but no native speaker would say it.
I suggest "Doing volunteer work is a precious gift for young students" or something like that.

No, it's not. That stuff is pretty lame. 

"Precious" is a misspelling of "precocious."