Do I need to plug in my hardware wallet to receive a deposit?

No, bitcoin is not stored on your hardware wallet.

A common misconception is that you must physically plug in your Ledger or Trezor to receive a deposit. You can always receive a deposit without using your keys.
 
Your bitcoin is stored on a digital address, and your key gives you access to sign transactions. You only need to plug in your hardware wallet when withdrawing bitcoin. Sometimes, we refer to hardware wallets as "signing devices" because that's what they do, sign transactions.