On 1 May 2011 I sent a tweet and then, a day later I deleted it. It's still there though because before deleting it I added it to Storify, and now it's trapped there forever. The take-home lesson from this is that even if a tweet's later deleted, once it's been saved in Storify it's permanently saved (you can also take screenshots etc).
I've never tried it in a blog post but am expecting it to work because Twitter's help files indicate that it should*. An embedded tweet inherits all the information that lets someone who's reading it on a blog post (instead of on Twitter) interact with it - they can favourite or RT it. If the tweet is deleted from Twitter this is no longer possible but the text of the tweet (and who sent it and when) remains.
Let's see... I just sent this and will soon delete it.
URL of tweet: https://twitter.com/JoBrodie/status/487658994925072385
This is a test tweet that I'm going to embed in a blog post or two and then delete. Only tested w Storify b4, 3y ago https://t.co/mjcI6xocLu
— Jo Brodie (@JoBrodie) July 11, 2014
Now to delete it and see what happens. (According to the info below if I made my account private that would have the same effect).
Now that the tweet is deleted you can see what it looks like above, and this is how it had appeared on this post before I deleted it from Twitter.
*"What if a user deletes a Tweet after it has been embedded on another website? Similarly, what happens to Tweets from users that change their Tweets from public to protected (or become suspended)?
In all of these cases, Twitter branding and Tweet actions will be removed from the embedded Tweet, but the content of the Tweet will still be visible."