Sorry I have to be a bit vague here. Suppose I need to know how to do something completely legal and ethical but have reason to avoid having the question connected to me to the knowledge of persons who may be looking for such questions. These people do NOT have NSA resources, but they are a lot more capable than a mere Google search. If I use Tor to create a new SE account with a throwaway address, do I need to NOT have the address on a domain that I own?
.. avoid having the question connected to me ..
.. do I need to NOT have the address on a domain that I own?
If you can avoid it, then by all means avoid it.
Whether you need to, depends on the capabilities of your adversary, but using the same domain that millions of others use makes you disappear much better than one that only you use and own.
(Unless you own yahoo of course :)