He would have hired a writer although obviously it would have been a much different character, likely only the same in name and basic concept. Depending on who that was who knows, Batman might have reached bigger heights or more likely died out after The Golden Age. But who knows what it would have been like for DC as a whole.
But how it would have affected DC as a whole, who knows. As bad as Batman comics were after WWII and especially after the early 50’s, him, Wonder Woman and Superman contiuing to be printed is the only thing that kept super heroes in the public eye until the Silver Age. Odds are if Batman had not been as popular someone else would have taken up that spot. Maybe Wildcat, Sandman, the Atom or who knows who else would have endured through the 50’s instead of Batman. But it’s also possible if whoever became the “non powered” hero in that spot wouldn’t resonate as well and the Silver Age as we know it never would have happened, or would have played out differently. Heck Superman especially owes a lot of what he is to Batman, as they teamed up regularly to this very day making their characters intertwined. Would Superman/Sandman stories have worked as well? Who can say.