Pretty much, especially if the friend is pivotal to the protag's origin story.
I've discovered some mind-blowing stuff just writing the first time meetings of characters that already have a long-term friendship at the time of the story. Or writing minor "adventures" they've shared - such as a day's tramp up in the bush that turns into an "overnighter" after a rain-swollen river makes it impossible to get home.
Just exploring how they coped with the situations and the bonds they formed in those events gave me strong insights into the way they interact with each other in later years.
Very little of what I wrote in the notes/early adventures was mentioned in the actual story I was writing, but the camaraderie and sense of a long shared history certainly manifested in the way they worked together.
You probably could get away with not saying specifically "why" she's important. Just that she is important, and that her death has affected the protag.
If something does come up that makes it clear why she was important (and this is why it's vital to know as much as you can, so that if/when that happens, your protag will respond appropriately) then the "why" will reveal itself.
For example, if your background-building uncovers that she is the one the protag always has turned to when feeling beset/lost/scared then any time in your story when your protag is feeling beset/lost/scared she will be wanting to turn to her friend but can't. If that comes through properly you won't have to say "she was the protag's rock and always willing to lend an ear when things got tough" you'll be showing how the protag feels having to cope without her.
edited 30th Jan '13 11:24:50 PM by Wolf1066