Definitely important!! You can't truly understand the culture just from what you read in books or the internet, or even what people tell you. You have to visit the origin of the culture and take it in for yourself.
To learn the language there would be most beneficial too since you'll be learning pretty much the way everyone is talking now, you know? In books or classes, they may only teach you the formal ways of saying things, which is good, but I'm sure you'd feel much more comfortable being able to easily converse with anyone.
On a sort of random note: When I was in Japanese school, my substitute teacher was Mr. One-Bear, (he was Native American) but spoke fluent Japanese cause he studied abroad. In his classes, they weren't aloud to speak a WORD of English!! But that's what allowed him to become fluent in the language. In America for example, they'd be a lot more lenient, which doesn't give you as much of a chance to practice Japanese since your comfort zone is with speaking your own native language. So studying abroad is extremely important, especially if you want to learn the language.
In Your Opinion...
