No, it is not safe. Online exchanges, online wallets are all not safe. Anything kept online has the risk of being hacked and stolen. Mt Gox and Cryptsy went down, Bithumb hacked, so keeping them in a desktop wallet would be more safe.
I recommend
Electrum and
MyCelium, both are secure and easy to navigate.
Even Blockchain.info or Coinbase are not safe!!! Stay safe and guard your coins well!