Is there a way to add "distinct" to SSMS IntelliSense?
No, I don't believe there is any way to manipulate the IntelliSense dictionary. And you'll notice other T-SQL keywords are missing from the list, too:

SELECT
DELETE
INSERT
FROM
GROUP
ORDER
JOIN
WHERE
HAVING


UPDATE is there, but only because it is overloaded (a function you can use inside a trigger to see if a specific column was updated).

Further, I'd have to wonder what is wrong with your data model that you're typing DISTINCT enough where auto-complete will have any impact on your productivity at all. DISTINCT really should be rarely used; almost every time I see it in a query, it's being used to remove duplicates caused by bad design or bad join logic.