No they won't die if not mated! Eggbinding is a real possibility though - they can die from that. They should always have a laying bin in their cages from about 6 months onwards, as they can cycle infertile eggs without ever getting a glimpse of a male. Are you thinking of getting a female too?
Eggbinding happens most often from husbandry issues although there can be physical issues that cause it too (such as fused eggs, eggs that are too large to lay, reproductive system deformities, etc.).