Is there a connection between celiacs and swollen salivary glands?

Unknown: Through a search i was unable to find a correlation between the two.

Could be: One of he symptoms with celiac disease is "dry mouth" due to the changes that occur in the composition of the saliva in the gland(see http://www.Medicinaoral.Org/wp-content/uploads/2009/08/medoralv13i9p559-doenca-celiaca.Pdf) this could lead to mucus plugs which could cause the glands to swell. Remember celiac is a disease of the digestive system and any part of that system could be affected.

connective tissue : Connective tissue disease: test for sjogren's (blood & sialogram) & autoimmune thyroid, explore with your doctor : there does not need to be one primary autoimmune disorder.

Celiac disease: This is an understudied area. Celiac disease has an autoimmune background and increased risk of oral mucosal and dental abnormalities. One study showed that celiacs have a higher chance of developing canker sores. This can cause swollen salivary glands. One other study showed lower chances of salivary cariogenic microflora in celiacs. So this is controversial. Don't forget to rule out sjogren's.