So far, I haven't tested the running time of the battery to flat, but it seems to cope well enough with my spot cleaning round the place. I'm generally just quickly chasing the dust bunnies in the hall daily.
I've tried the tool adaptor with the DC02 wand / DCO2 mk2 floor tool, and I still have reservations about the weight, but it seems to work well enough. The DC31 is supposedly 38AW/65AW (10 min/6 min) and on full tilt managed to pick up some heavier pieces (broken bits of crayon) up the wand okay.
The only other issue is that the tool adaptor is a bit slack in the top of the DC02 wand allowing it to wiggle a bit. I'm going to keep my eyes peeled for a generic 32mm aluminium tube and if it isn't snug, I might just glue the adaptor into one of those. Even if it means I have to buy another adaptor for the convenience of robbing other tools from other vacuums in the house!
I am wondering if it'll power a small turbo brush though....