I'm wondering whether actions within an action chain can trigger additional actions before moving to the next link in chain.

To put it simply, if I play Cloying Quagmire (2 damage to target and target becomes corrupt) in response to an action (call it a1), while having a Tainted Well in play (action: whenever a unit is corrupted, you may assign 1 damage to that unit), will the well add 1 to the damage dealt for a total of 3 damage before a1 resolves?

No, you can't interrupt the resolution of an action chain to play additional Actions. The general understanding we have is that you have to play the action from Tainted Well after the rest of the stack resolves.

I'll talk to Lukas and have more clarification on this later. There are TONS of cards that have a similar wording and similar timing problems.

Officially, the way to use these cards currently is as I said in my above post, at the end of the action chain. There may be some additional clarifications or tweaks to this in future FAQs though.