@demoskinos: Just a question there, because I think you might be saying something you don't mean.
If I want to use Miku in my product, lets say I'm selling headphones and I want to use her. I have to pay for her right? Her image, her likeness? I must have to pay something to use her in my product or advertisement. So I'm paying a company for licensing her.
So when Beats decided to release a Justine Beiber version of headphones and those Lady Gaga ones, they paid someone to let them use Beiber/Gaga's name and image.
So really, anyone can use any musician as long as they can afford it. I mean, she's not really any more open source than any other musician right?
That's actually one of the most incredibly complicated aspects to Hatsune Miku/Vocaloids since they exist both in image and in software and there's different rules for her official image/software and adaptations/works generated out of Vocaloid software. I'll try to compartmentalize it based on your hypothetical scenario.
Most relevant to your Beats question: the official image of the Vocaloid characters (illustrations, etc.) is almost entirely freely available via the Creative Commons Public License (offsite URL: http://piapro.net/en_for_creators.html) ; however, this applies for non-commercial use only, so that excludes your Beats use case.
With regards to commercial use, they have an item on a FAQ in the aforementioned link:
Q: What should I do if I would like to use the Characters for a commercial purpose?
A: Please contact Crypton atintlbizcrypton.co.jp for information regarding commercial use. But please note that we will not respond to questions requesting information that can already be found in this FAQ.Credit http://piapro.net/en_for_creators.html
So I suppose if you wanted to monetize Hatsune Miku's "official image" (such as the one I just posted above) with your Beats deal, you'd actually have to approach Crypton. This has been done by Toyota and I think Pizza Hut, etc.
One very interesting note is that Crypton actually at one point declined the use of Hatsune Miku's image on a Japanese political campaign because they didn't want Hatsune Miku to be associated with any sort of politics.
CCPL, however, may not apply in the above form if you create your own . YOU/your label/etc. have the rights, to my understanding.
It gets kind of amazing but even more complicated here: if you want to use a derivative image/music (so for example an image off of someone else's DeviantART or a song on YouTube), the rights and licensing is actually up to the artist/group that released the original artwork/song based on the image or Vocaloid software.
I hope this addresses your questions.
EDIT: Full disclosure: I'm very license conscious since I have to deal with a lot of *nix in enterprise applications, and software licenses can get really crazy between Linux/BSD/Oracle software/distros/etc.