Take the argument to the extreme and consider something like and iphone 5s. It has a tiny sensor so everything is always in focus. But it still has an f2 lens in terms of light transition. So sometimes I can get a better macro shot in low light on my 5s than I could on my 5d mk iii. Because to get an equivalent depth of field I'd have to stop down to f18 which would push up the ISO to extreme.
Fine. Now, because image noise is determined by the total light gathered, which is proportional to the area of the sensor, you have to figure in the effect of sensor size on ISO noise. What that means is a shot on the iPhone 5s at base ISO (ISO 32) has the same level of noise as a shot on your 5DIII at ISO 1600. Want to see what the noise at max ISO on the iPhone 5s (ISO 3200) would look like on the 5DIII? Set ISO 102400 (H2) and push the exposure 2/3-stop in post. Ok, the iPhone doesn't look that bad, but that's only because of massive NR that obliterates the detail in the iPhone shot.
So, no - there's no DoF advantage to a smaller sensor.