Can TREZOR sign transaction with input address beyond gap limit?
Yes, you can sign with that. Hardware wallets don't care about your gap limit, they aren't deriving individual keys when you setup the wallet. Rather they just store the master private key (or the seed used to derive the master private key) and then derive the individual keys needed on-the-fly. So if you tell it to sign with the 999,999th key, by giving it the correct derivation path, it will do so without complaint.