Even though is hard to establish the exact size of the English lexicon, this is probably not the case. The main reason is that Esperanto is a relatively young language, while English is much older and has absorbed influences from French (from Old French after the Norman Conquest, but also from more recent varieties of French), Latin, Greek, Dutch, Italian, and from several languages spoken in the former colonies. There have been claims about the English about the English language having a million words.
For comparison, this Q&A document from Esperanto USA says that the Plena Ilustrita Vortaro contains 16,000 root words and that Esperanto's word formation techniques allow this number to be expanded to around 160,000 words. However, I don't know how you would come up with Esperanto translations for malapropismmalapropism or sciolistsciolist, though I certainly hope so.