Some have a concept of it for sure, spent their youth at the club coming through the ranks, come from working class families that are lifelong fans. Jack Grealish springs to mind, think he was born just down the road from Villa Park, and he himself is a lifelong Villa fan, or Kane, grew up just down the road from WHL, most of his family are Spurs fans I thought? Not many have the skill/athleticism to make it however.
But yes the majority of footballers, for sure, it would be hard to have that context, especially the passion in derby's. You could argue even the passion today for the fans is diluted from the old days when it was say Millwall shipyard workers vs Hammers shipyard workers. Today it is millionaires kicking a plastic ball around, with the fanbase spread across the globe.