Still not real good practice. You're relying on a diode voltage drop of 0.5-0.6V. In reality the drop with vary depending on the current drawn through them. At low currents, the drop might only be around 0.2V. The datasheet for the diode will have a graph of forward voltage drop vs current.

Also if the battery voltage starts to drop so will the output voltage. LDO regulator won't have this problem until the battery voltage goes below the minimum input voltage.