No, I have my account with 4 other people at 3 different addresses, it works just fine. Keep in mind all of these people are in the same city, though...
[edit] Note for other post: you don't have to share actual accounts - you can invite people to share prime membership; they will use their own account to do their own shopping but still get the same perks.
[edit] Note for other post: you don't have to share actual accounts - you can invite people to share prime membership; they will use their own account to do their own shopping but still get the same perks.