It can. I don't think it will.
We know it can because it's happened before. Stories like Robin, Gotham Central, Nightwing, Harley Quinn, Shadow of the Bat, Gotham City Sirens, and more have been told, often with critical and commercial acclaim in the past. We know a Superman show can do quite well without Superman from Smallville's 10 year run, despite much of it being weak. We know it *can* survive, even thrive without Batman.
But this series seems to have made two mistakes. Our 'surrogate Batman' Jim Gordon is largely a cipher, less interesting than Bruce Wayne, with less backstory, less pathos. This doesn't work in a franchise whose themes involve such colorful personalities to have the main guy so... uncolorful. This is correctible, exploring Jim's backstory, which sounds interesting sort of, handles all of that.
But moreover, the larger problem is that Gotham is already home to nearly all of the craziness that Batman deals with. The show has already set up the need for Batman so profoundly, it's no wonder there are already themed vigilantes roaming the streets. In the Nolan films, divisive as they can be at times, it was clear that the Wayne's death helped rally Gotham from descending into chaos in the twenty years between the Wayne's death and Batman's arrival.
The series, imho, should have been a much more grounded crime drama that happened to be set in Gotham City that over time grew into the Gotham that we all know and love. Colorful personalities, yes, Gotham landmarks, yes, the groundswell of theatricality in the DNA of the city (Waynes were murdered in the theatre district, weren't they?), absolutely with Jim Gordon gaining early victories by rallying the city around the Wayne murder before the city begins to fall to the big bads of subsequent seasons, setting the stage for Batman, but more importantly, changing Gordon on a fundamental level from a crusading 'white night' into a tired white haired man turned old in four years time, like a President.
As is, from what I've seen of the first three episodes and heard about later ones, it looks like Gordon going up against a lite version of Batman's rogues and problems. Viper that does the same thing as Venom. That, to me, is not interesting, because then the show becomes a less interesting version of Batman, prompting threads like this one. Can a less interesting version of Batman work? No, no it can't. Can something fundamentally different from a Batman story occurring in Batman's sandbox work? Can there be a great awesome prequel to Batman that explores the city and the world in a way that makes everything awesome but it also entertaining in his own right?
Would this work better with a focus on young Bruce? Possibly. He's one of the best parts of the show, but this show can't really be shifted into a 'Smallville' or the weird Lord of the Flies/Hunger Games version of Smallville that the world of Gotham would turn it into. Right now Bruce is like the backup story in the backs of old comics. He doesn't really directly relate to the main plot, but he's an important feature to complete the audience's entertainment. He honestly could spinoff into his own thing, a road show of some sort, and I'd happily watch that over Jim Gordon doing Batman's job ten years too early.
I don't hate the show, honestly I don't, but I also am losing interest, and I have some clear ideas as to why.