I think it would majorly depend on who owned it and who produced it. For one thing, if it wasn't produced in-house by the networks, it would have been liable to be majorly screwed as far as scheduling.
As a standalone IP, you bet Lauren and the rest of the crew would have had much more creative freedom. For one, there probably would have been a much larger adventure component to the show than there already is, a tighter continuity, and more flexibility as far as planning the episodes. There also would have been more room for experimental storytelling, but this has just as much potential to backfire ("Feeling Pinkie Keen") as it does to do good. The benefit would have been, depending on the theme of the show, that it could have allowed for a better context for more complex morals than presenting them as friendship lessons.
In this hypothetical version of the show, toy mandates from "A Canterlot Wedding", "The Crystal Empire", and Princess Twilight to even the Crusaders (originally intended to only consist of Apple Bloom, in development named "Appleseed") would not have happened. I also have no idea how the slice-of-life and fantasy elements would have been balanced or interwoven. They would more likely have been interwoven under a tighter continuity unless network mandates would demand otherwise.
As for the fanbase, MLP has a built-in support base of legacy collectors from the earlier generations and people who grew up with the nostalgia of the older shows, so that component of the fanbase would not be there. Nor would anyone else who jumped on purely to investigate how something with the My Little Pony name could overcome the inevitable stigma attached to it.
However, if there's anything that the success of shows like Adventure Time, Steven Universe, and Gravity Falls can tell us, it's that the right ideas can pull large amounts of fan support even if they aren't tied into 30-year-old franchises from other media. So even though the composition of the fanbase might have looked a little bit different, I still think the show could have been very successful on a large scale. But still, that goes down to the specifics of what exactly a non-MLP FiM series would look like.