Load Bearing Weight Capacity of a 3/4“ x 3/4” Wood Molding?
You don't mention what kind of wood you're planning to use, which does make a big difference in this case but assuming you're going to use pine/poplar or some similar readily available wood my answer would be no, the 3/4 "cleat" is not going to hold up. My first thought is that if your dimensions are limited in the way your drawing implies, what about a piece of angle iron, or something similar?