Challenge Log is completely separate from your Grand Company - there are entries in the Challenge Log that reward you for doing certain things for your Grand Company, but your GC promotion is not based on that. Ranking up in your Grand Company requires Company Seals that you can simply get by going around and doing FATEs, plus certain ranks (particularly higher ones) require a quest to be completed along with undertaking a certain dungeon and completing the first two levels of your Grand Company Hunting Log (the third one is not required for a promotion). So basically, don't worry, you don't need to have a Crafting class to get a promotion in your Grand Company.

This page has all the information about Grand Company ranks and what you need to do to get a promotion.