It's sufficient but not necessary. It would be better if there was an entity like the library of congress who would keep it safe, but private until copyright expired after which it would become public. Right now piracy leads to way more of free entertainment than preservation.
In practice, it's necessary. While escrow should absolutely be a requirement to receive the benefits of copyright protection you'd also need to make sure that the escrowed artifact is actually complete and in a usable form and covers every version of the work. That means a lot more than dumping it onto the library of congress so even with that requirement we would benefit from independent archival.