My thoughts on the matter:
Crossmedia Stuff is all the rage at the moment. Still no project to date seemed to really set the world on fire. Most crossmedia projects involving games where TV Series <-> Game Series crossovers.
There are some real problems that might hamper crossmedia projects having the imagined effect on sales in both medias:
1) different medias might have different audiences. Just because someone is a total Zombie Game fan doesn't mean he is also into watching a Zombie TV Series weekly. And the other way around. In this case all the crossmedia effect is gone.
Same could be said about bands and games. There MIGHT have been a larger proportion of gamers being metalheads in the past. Nowadays I guess that the gamers musical taste is pretty much as diverse as the one of the rest of the world. So you might have reached a larger amount of metal dudes that wouldn't have played the game else. The same cannot be said about gamers not into metal. They might still play your game, but they will dead certain not buy the record if they are not into metal to begin with.
You might get some metalheads interested into that obscure metal band nobody heard about, true. But is that worth the amount of money needed for game development? Which brings us to the next point...
2) Game development costs A LOT. Of course, developing a tetris clone for iOS is quite cheap, especially if you don't worry about the bugs. But if you are talking about 3D FPS and MOBA games with decent to good graphical quality, you are getting into the 1M$+ range quickly. Good things can be done for less, but then there are compromises involved.
And as you want to use this game also for advertising purposes, I would guess you want to reach as many gamers as possible. Which means mainstream not Indie. Which means AAA budgets and big(ger) studios.
Your best bet is to see if you could reach a mutual agreement with a studio developing a titel anyway, early in development, to see if they are interested in using such a "Band Skin" for their upcoming game. If the Band is famous, they might go for it, as it might also help sales of their game. Then you MIGHT not need to pay for it.
A mod can also give you the "Band skin" for less. Problem is, someone still needs to do the art. And that is one of the more expensive parts of game development (apart from marketing which is eating up more than half the total cost AFAIK).
3) You really need to make sure you get someone designing the game that knows what he is doing. There are enough cheesy movie adaptions out there, or other games with famous brands that where cheaply produced before. A lot of them plainly sucked, leading to gamers generally not buying movie adaptions anymore, until somebody told them this specific adaption really did not suck.
You need to make sure the genre and the whole expierience matches the bands image, else it will look cheap and dislocated. For death metal bands that use gory imagery on their covers and violent language in their songs a shooter or moba might fit quite well, and with some slapstick humour you might win one or two points with your audience (Death metal rockers slaying zombies with their "axes", anyone? With an electrifying special move? 
)
A cutie girl group in a violent shooter though... no. Just no.
That all said, there have been GOOD examples since like... forever.
Rock'N'Roll Racing - Inspired kids from my generation to get old 70's Hard rock and early 80's Metal CDs from the library and listen to Steppenwolf and the likes. This game now REALLY matched an EXTREMLY good sound quality for the time (only 4 Hard Rock tracks, but I be damned if this wasn't the best sound you ever heard from the Super Nintendo, EVER) to visuals which where quite good at the time, and really heavy metal in style. Add to that an actually quite fun action racer, and you had a game that not only sold old Hard Rock songs to a younger generation, but was also one of the best action racers on the console.
Brütal Legend - Marrying the humour of Jack Black, his knack for Rock and Metal, and a as far as I heard quite entertaining game. Haven't played it yet, certainly will at some point. AFAIK Jack Black and the ingenious way how the main protagonist was created in his image, together with the way the whole game made fun of the sometimes quite OTT ridicolous Heavy Metal imagery, sold the game.
I am sure I could find more if I went looking, these were just examples I remember. Maybe not the kind of crossmedia creations you had in mind, but good examples on how to do it, the right way.
