Not sure why this would not work, so I'm just going to give a little background about how these 'boosters' work so you can decide for yourself.
As you shower or bathe, you open a faucet to mix hot water from the tank with cold water from the city, producing a comfortable mixture. The hotter the tank set point, the less hot water you need to draw to produce a comfortable mixture and the longer you can shower.
The tank temperature has nothing to do with this component. Even without this component, you can "boost" the amount of hot water in your house by increasing the temperature of the tank.
There are however major risks to increasing the tank temperature. Notice that it takes only 2 seconds of exposure to 60C water to produce the same amount of burn as 1 minute of exposure of 50C water.
For this reason, it is really unsafe to simply boost your hot water temperature. A baby (yours or someone else's) may come in and turn on your hot water tap. Or drunken you may do the same. This may lead to serious injuries. It is therefore against code to have high-temperature water flowing out of a tap.
The way this component (a mixing valve) "boosts" water is that it allows you to keep the tank at a high temperature but it ensures that the water coming out of the tank (and into your faucet) is mixed with cold water automatically shortly after it leaves the tank.
This "booster" is a safety feature that allows you to meet code requirements and stay safe.