Storing AES encrypted RSA private keys on a server
Given that you used a strong password to derive the AES encryption key: Yes you could securely store your RSA private key in encrypted form on a server. BUT, since there is no technical need to have your private key on the server, why would you risk it?

Look at it that way: Suppose you have very sensible data (like private photos or so). Now you could encrypt it with a strong algorithm and password and send it to all your friends, knowing that no one would be able to to decrypt it. Anyways, I personally would still not do that. Even if I trust the encryption, I would not unnecessarily give encrypted data to someone else for no good reason.