I guess I will chime in since Jim called me out.
I agree with Dave, 8x seems like quite a stretch. Unfortunately I have not played with alkaline cells to know how they handle discharges, but the internet comes to my rescue because someone else has already test this and I can reference his work [1].
There are a few different things to consider.
First, what is the real cutoff voltage for your widget? Most (complicated) widgets are running their battery input through some form of massaging circuitry and probably actually have a wide window that they can operate. Most simple widgets (aka flashlights) will just keep running but get dimmer until they batteries really give up. I think the 1.4V cutoff listed in the article is a little bit high. Looking at the actual discharge curves if your device threshold 1.3V then there is still half of the chemical energy left in the battery. This chemistry appears to hold its voltage pretty well until it knees just under 1V and then it tanks.
Second, what is the effiecency? A decent switch mode converter can get around 90% effiecency. At lower voltage the switch mode converter has to work harder and pull more current to achieve the boost ratio. This quickly becomes a vicious cycle because the more current you pull from a cell the more it drops which means that your boost ratio needs to increase which causes more current. This will decrease the energy left in the cell by a bit.
I have a couple of major problems with this idea as a whole.
First, how much noise does this inject into the device? This is a very tiny switch mode converter which means that the inductors and capacitors are very small and can't hold much energy so therefore can't prevent much ripple. Normally batteries are considered a very stable voltage source so filtering may be reduced on battery powered devices.
Second, as a user I have no indication that my batteries are almost empty. This boost conversion is done at the cell level so the device always thinks it has a full battery until the cell is totally dead and I have to replace them. It means that I can't plan ahead to replace the batteries. I either have to keep extra cells on hand or be willing to go without by device until I get new cells.
Ray Scheufler