No but neither does WhatsApp. The reason for this is that it's incredibly hard to properly do end-to-end encryption with multiple devices. It's a trade-off you have to accept if you want secure end-to-end encryption.

The way it works with WhatsApp and Signal is that your key is generated on your phone and never ever leaves it. The web client actually establishes a connection to your phone and routes all messages over it.

Now, the Axolotl ratchet protocol does support encrypting messages to multiple keys (it's what they use for group chats), but doing it properly requires time and effort in order to remain secure.