Can you deposit to an unplugged Trezor?
Yes.

When you initialize your Trezor, it generates a private and a public key. Private key never leaves the device (that's the core value proposition). That means you can't sign transactions (spend coins) without Trezor plugged in. However, the web wallet can remember your addresses (derived from the public key). Even without the Trezor plugged in, you can check your balance and send coins to your addresses from elsewhere.