In which case, why bother storing at all?
If our committed individual merely cycles until hitting an account with some "cash", cleans it out, then moves on to the next. I see it is still highly likely they would not hit anything worth their time, currently. However, further down the line, with many many addresses being used and serious money at stake, one can imagine this becoming more and more plausible as an organised, (illegal), revenue stream.
In which case, it becomes a matter of simply how many BTC address can you compute and check per second say. The situation under which will only get worse as technology advances.
Bear in mind, we are not looking for a single address among the clouds here. We are looking for -any- address containing BTC.
Addition - If this becomes widespread, users would spread their BTC across multiple addresses, which effectively makes finding an account with BTC easier, but at the same time, reduces the proftability of any particular "hit".