Can candida over-growth occur independent from a leaky gut? Or does candida over-growth always cause a leaky gut?
Good question. I think the term yeast overgrowth is somewhat misleading. Any amount of yeast in the gut is not a major problem by itself. It is only a problem if it turns hyphal (fungal) and invades your intestinal wall. This often happens when antibiotics kill the bacteria residing in the intestinal mucosa, thereby allowing Candida fungus to colonize the bowel wall. It can also occur if you have a depressed immune system. So in answer to your question, no, a simple yeast overgrowth will not necessarily cause a leaky bowel. However true intestinal candidiasis is not just an overgrowth of yeast, it is colonization of the bowel wall with Candida fungus. In my opinion, if you have intestinal candidiasis, then you will always end up with leaky bowel.
It seems to me that gluten intolerance/sensitivity, candida and leaky gut are all connected to each other.
Candidiasis is certainly linked to leaky bowel (see above). Genetic gluten intolerance can also cause leaky bowel. A leaky bowel can also cause gluten intolerance due to partially digested peptides crossing from the gut into the blood and confusing the immune system, triggering a gluten allergy that didn't exist before, or at least was so minimal you never noticed it before.
X factor depressing immune system = gluten sensitivity = candida overgrowth = leaky gut
I would modify that slightly:
X factor depressing immune system -> candidiasis (Candida fungal infection of bowel wall) -> leaky gut -> gluten sensitivity.
If this is true, then in theory once you get the candida overgrowth in check would that heal the gut as long as the person avoids any offending foods?
As I said above, it is not just a yeast overgrowth that is the problem. You need to eradicate the fungus inbedded in your bowel wall. This is easier said than done. However, in principle, yes, if you can eradicate the Candida problem and heal the leaky gut then your allergies to many foods should eventually disappear.