I have read that Nathan Hale was immediately recognizable to all and universally regarded as the most handsome man in all the colonies.
He was like a rock star and known on sight by many people he had never met. When being taken into custody someone in the crowd yelled his name and waved. He couldn’t deny that.
A worse choice for covert activities couldn’t have been made.
It depends on what he was doing, was he gathering the intel as an invisible man sneaking around into hidden and forbidden places, or as Nathan Hale in whatever life he was already living?