Of course you can. Yes, once you complete a Ph.D. in English, you will not need a bachelor's degree and you will not need a master's degree when you search for a job.
Entry into a Ph.D. program in English may be done by those with bachelor's degrees in other, related fields. Or by those with appropriate experience outside academia.
And let's face it: Once you are awarded the Nobel Prize in Literature, practically any English department will hire you as a professor, even if you have no degrees at all.