Can private data be encrypted and stored safely in public? Given that AES-256 is reasonably strong encryption, can private data (for example Bitcoin private keys) be sufficiently encrypted and stored safely in public places (for example a public github repository)?
The short answer is: if and only if the key is never compromised and the algorithm is never severely broken.

To inject some realism into this question, one real-life event that's worth knowing is how Wikileaks' encrypted file of USA diplomatic cables got compromised.  Bruce Schneier had a good summary at the time (it's not a primary source, but he links such sources).  But the basic idea is:


Wikileaks encrypts a file with lots of sensitive information, using password-based encryption.
Wikileaks shares the file and password with a journalist.
Wikileaks posts the encrypted file into Bittorrent as a backup/survival measure.
The journalist, who is not technically savvy at all, writes a book and uses the password as a chapter title.
Observers manage to put two and two together, download the torrent, and decrypt it with the password from the book.


How does this address your question?  Well, if the file had not been uploaded to a public system like Bittorrent, the damage from the exposure of the password would have been much smaller.  So publicizing a ciphertext widely certainly carries additional risks.

That's not a yes/no answer to your scenario, because there isn't one.  Restricting the circulation of the ciphertext is always safer, but this is really a risk vs. convenience tradeoff where you might reasonably opt for convenience, depending on the application.