I think Ethereum might work even without consensus. For example, consider the toy model:
Totally 2f+1 validators, f validators are dishonest, f+1 are honest. The only difference of the transactions records in the f+1 honest validators is the order of the transactions arrived because they are honest. Which means the transactions in the f + 1 validators are ACTUALLY the same finally despite the difference of the orders.
So the client checks the transactions from the 2f+1 validators, after a while, he will find out despite the difference of the orders, the transactions are the same at f+1 validators, so he can confirm some of the transactions.
Though the model looks rough, but I just wonder is the consensus necessary for Etheruem?