Very, very few people are going to have a social network that does more than get a foot in the door.
Typically, referrals have positive impact like making sure your application gets looked at by a human and possibly tips a "maybe" into the candidate's favor for scheduling a phone screen or moving to the next round of interviews.
There are plenty of very talented people with large networks of former coworkers who will attest to their capabilities and give them referrals, who nonetheless are still struggling to find work.
Typically, referrals have positive impact like making sure your application gets looked at by a human and possibly tips a "maybe" into the candidate's favor for scheduling a phone screen or moving to the next round of interviews.
There are plenty of very talented people with large networks of former coworkers who will attest to their capabilities and give them referrals, who nonetheless are still struggling to find work.