Absolutely!
Allergies cause generalized seborrhea which in the end makes the glands overproduce their secretions.
Any dog can develop an allergy to a food that they have been on for many years, at this point it was a good idea to try a different protein source.
Good bowel movements are also important for the anal sacs to empty, if your dog has loose stool it will be difficult to push out the anal juices from their sacs. Having more fiber in the diet can facilitate the expression.
From Merk Manual:
Anal sacs may become impacted, infected, abscessed, or neoplastic. Failure of the sacs to express during defecation, poor muscle tone in obese dogs, and generalized seborrhea (which produces glandular hypersecretion) lead to retention of sac contents. Such retention may predispose to bacterial overgrowth, infection, and inflammation.
From Science Direct + Small Animal Dermatology (Fourth Edition):
Anal sac disease is a disease process that results in anal sac impaction, which may be followed by secondary infection (sacculitis) and abscess formation. Recurrent anal sac disease is often associated with underlying food hypersensitivity or atopy. It is common in dogs, with the highest incidence noted in small-breed dogs. It is rare in cats.