There are many Toxic, hereditary and other immune issues that...Thyroid INCLUDED, that, IF properly tracked [meaning all the docs ASK THE RIGHT QUESTIONS?-tho usually not] that causes for most immune diseases can have the source issues found. HOWEVER? WE are NOT HOTHOUSE FLOWERS! Contained in any controlled environment, nor carefully monitored when fed..etc.
Do not forget that the genetic variables in terms of disease resistance - 'programming' in each of us varies by the BILLIONS. For most of us, myself included, it comes down to timing and the luck of the 'draw' as to how it all effects/affects our bodies.
As for your belief that it ties into Celiac's? So far, research seems to have only been done on RAT BRAINS w/no mention about the digestive aspects at all. While this might apply to YOU, it's not a 'one size fits all' aspect of diagnosis. Take a gander at this menu and see IF any connections are found so far...to date?
http://neuromuscular.wustl.edu/alfindex.htm
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1279673/
Treating Hashimoto's is like treating cancer in many ways....prudence in administration of therapies can be wise, tho sometimes while dosages are adjusted? A certain chain of events...in this case the thyroid can still continue to cascade-the train is set in motion, so to speak. Therefore diligence if follow-up testing and treatments is necessary. This, aspect tho, unfortuneately isn't done as diligently as often needed. Either due to inexperience or lack of follow-up by the patient or physicians involved.
Back to the post? Synthroid has essentially slowed damage to my now dead thyroid for 20+ years. Just make sure you pay extra [usually these days?] for the GOOD stuffs, not the generics. All the best - j