Would this method allow fast authenticated encryption using only a single encryption operation per block?
This does not meaningfully authenticate the ciphertext. Your encryption is the same as OFB, meaning no block depends on the previous plaintext; for instance, $$C_2=P_2\oplus E(P_1\oplus (P_1\oplus E(IV\oplus 0)))=P_2\oplus E(E(IV)).$$ That means confidentiality should be fine; however, it provides no authentication except of the length of the message.