That 800mAh is REALLY misleading. The thing has 2 420mAh lithium cells in it. Therefore, they said "well 2 times 420 is like 800!"
But LiPo cells are 3.7V. So to get 9V out you need a bit of a boost. At 9V the capacity is only about 345mAh. Which is fine for pedals, but it means you will be recharging fairly often.
The bigger problem is the boost converter will insert some noise into the system, not the dead steady output of a true 9V.