Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
The answer to the first part (Should) is obviously, "No!", but I'm reluctant to test the possibility for that very reason.
You can't vote (up/down) for your own post.
But you still can vote to close, reopen or (un)delete your own posts.