No, Stack Exchange does not appear to make any claim to denying any three-letter agency access to data that they've requested legally. Quite the contrary:
Here are some of the ways we may use personal information you provide us:
- To transfer information to others as described in this policy or to satisfy our legal, regulatory, compliance, or auditing requirements
In the United States, this is fairly standard, if rather unfortunate, as, after all, the US intelligence community has put a great deal of time and money into building an enormous capacity to spy wherever it seems to be necessary, and has a lot of legal force behind its demands.
Some organizations deliberately ensure that no protected data is accessible even to the organization's staff (e.g. the famous Lavabit), but this is utterly impossible for SE, which routinely uses individual personally-identifiable information for communicating with users, catching abuse, and so on. None of this can be made to require an active login session to work. So not only does SE not currently make any such attempt, it almost certainly never will.
See also Privacy Shield Principle 1.a.:
An organization must inform individuals about:
xiii. the requirement to disclose personal information in response to lawful requests by public authorities, including to meet national security or law enforcement requirements
So this is baked into the Privacy Shield framework.