If the DIY
overflow will not auto start then there are plenty of hang on overflow box's that will auto start again.
I like the U tube overflows better than the Clam shell style overlfows because the U tubes dont need a powerhead to restart the syphon.
If the ends of the U tube remain under water then the U tube itself will stay full of water and the syphon will start back up when power is restored. Should power go out for such a long period that water evaporates out of the overflow so the U tube end is exposed to air and it empties then NO
it wont auto start but honestly power would have to be out for days for this to happen.
The key to make sure the U tube stays full of water is to make sure the ends of the U tube remain under water. How to do this? Well on the outside portion of the overflow you should put a baffle about 1/2 way up the u tube splitting the drain area off from where the U tube will sit. This will force the area of the U tube to be 1/2 full all the time. Make sure the the U tube is long enough that the end is a couple inches below this baffle wall.
For the inside portion of the overflow make sure the box is also deep enough so that its a few inches below the outside box's baffle wall and also make sure the inside portion of the overflow's U tube is lower than the outside baffle wall. This will cause the water level in both parts of the overflow to equilize at the level of the outside baffle wall when power is out and thus the U tube remain full of water.