No, I don't think so. Wax is made de novo from sugar.
These are not thinking issues. I tried to find researches about pollen and protein but they all have cost.
Every wax information says that bees need pollen to make wax. Even if wax does not include protein, synthesis and running entzymatic systems use proteins.
All enzymes are proteins.
Australian researching tells that when hives have longtime heavy flow, the brooding of colony collapses. They have thinked that continouous exreceting of wax is so hard job, draw combs and cap them - . They move hives to some pollen pastures that the colonies recover.http://www.bee-hexagon.net/files/file/fileE/Wax/WaxBook2.pdf
WAX BOOK 17 pages
Wax production and comb construction activity in the bee colony are determined by following factors:
• Nectar flow: the greater the flow, the more combs are needed for storage.
• Brood rearing (egg laying): the more eggs are layed, the more comb cells are needed.
• The presence of a queen: only colonies with a queen build combs.
• Temperature: temperatures higher than 15° C favour comb building activity
• The presence of pollen as a protein source