I'm confused as to what you mean. Are you asking whether emailing a popular youtuber is worth the effort? Most popular youtubers wouldn't have the time, I don't think, to answer all the emails they get from fans.
Sounds a bit too desperate and unprofessional to me. Any old Joe could write an email, chances are they won't bother with it.

Better idea would be to see if they have a PO box and then write them a handwritten letter. Looks very friendly and shows you've put effort into it, making them feel obliged to reply :)
does emailing a youtubers on their gmail is a great idea?

Absolutely NOT if it's asking for a shoutout. That would be unprofessional and self destructive.

Questions however are fine, no one is going to bite your head off for a question. At least, I wouldn't. But I am also not a huge YouTuber.
Yeah big YouTubers don't have time to do all that BS...only time I'd see them promote anyone is a real good IRL friend, and not even a shout-out like include them in their video or something is what they would do. Or collaborate with them..and that's only in real life best friends lol
It depends on the purpose of the mail, and how big the channel is. I've managed to contact relatively big channels, between 50-100 thousand subscribers, but never higher than that. Although it is worth the try, if it's something that you think will interest them :)
the only people that email me are networks lol.
there's no harm In trying, I know a few that read their mail, but if their subs are in the millions it's probably not worth it as they likely get spammed a ton