Can you deposit to an unplugged Trezor? I just want to confirm if my logic is correct. If I send Bitcoin to my Trezor address while the Trezor is unplugged does the web wallet then receive the private keys from the transaction and only once the Trezor is plugged in again are the keys taken offline? Also access to the web wallet is impossible without the Trezor I assume (ignoring recovery seed). Technical answers are welcomed!
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.