I very much doubt that. To achieve what he did, Van Leeuwenhoek would have needed to: have technical skill; be literate and sufficiently educated; have connections to get published; have access to material resources; have lived in a time of exploration; have lived in a place of freedom of expression; be of the required gender and race; have sufficient free time; and surely a certain amount of luck.
How many others would likely have already considered - perhaps even tried - to look for tiny living things, yet lacked one or more prerequisites from the (incomplete) list above? Nick Lane cannot be refuted, yet this quotation almost certainly does a disservice to the truth. Good and bad ideas are everywhere all the time; Van Leeuwenhoek deserves credit, but only for his execution.
Here's a BBC science documentary from 2009 called The Cell that begins with the story of Van Leeuwenhoek. Unfortunately, this YouTube copy has been dimmed presumably to avoid a copyright takedown. It's a shame these documentaries languish in the BBC archives.
Narrator:"My starting point is September 1674 and the Royal Society of London. A mysterious satchel arrived in this club for gentleman scientists. It had taken five days to get here from Holland, across the North Sea by ship and then by horseback rider. The package came from a man who built the world's most powerful microscope, a microscope that revealed a hidden kingdom no-one had seen before..."
