It is definitely possible to go your whole life without having sex. Much like it is possible to go your whole life without loosing your temper. It may not be easy, but it is definitely possible.
But all of them appear to be "core" desires to us because they are immediate, potent forces. But just because these appetites are strong doesn't make them necessary. Everyone has to eat something but (in the general case) "you don't have to eat that *right now*" is true. Same with sleep - you don't need to sleep as much as you think you do (and you probably should be sleeping some times when you don't feel like it). So we come to sex. Is sex necessary for the continuation of the human race? Yes. Is it necessary for you to have sex at all? No. (Again, in the general case).
But all of them appear to be "core" desires to us because they are immediate, potent forces. But just because these appetites are strong doesn't make them necessary. Everyone has to eat something but (in the general case) "you don't have to eat that *right now*" is true. Same with sleep - you don't need to sleep as much as you think you do (and you probably should be sleeping some times when you don't feel like it). So we come to sex. Is sex necessary for the continuation of the human race? Yes. Is it necessary for you to have sex at all? No. (Again, in the general case).