Don't know exactly, but I worry about the chances of that enough given the current state of third party infrastructure that I'm keeping every last bitcent I own right now in offline wallets.
Bitcoin has an anti-pathy towards 3rd party infrastructure at its core ... 3rd parties need to figure out ways to become useful without requiring complete ownership of private keys, like blockchain.info approach that keeps only keys that have been encrypted on the client side. There are many other approaches that can allow for services to be delivered without 3rd party having total access to private keys, multi-signature, time-lock escrow, smart contracts and etc.
3rd party control is a bad approach modelled on old ways of handling money, it doesn't need to be like this any longer with a crypto-currency public-private key-pair as the ownership basis. Providers need to think of service+owner business models ....