Oh, he exists. He's a program from the very first iteration of the Matrix (the utopian paradise that didn't work because nobody bought in). He appears and spontaneously gives people stuff? For free? Yeah, sounds like something utopian to me.
Realizing just how ludicrous the concept is and how adults quickly see through the idea of Santa, I like to think that the Architect repurposed him as means to assert control over young minds in later iterations of the Matrix. The Naughty List is basically made up kids who question their reality, and belief in Santa enforces conformity while simultaneously rewarding compliance with the system. He's the carrot, the Agents are the stick.
Frankly, everything about Santa fits the Matrix.