Superficially, the answer to this question is, obviously, yes. We reason spatially and with mental simulation, but we also reason by applying the linguistic conventions learned from our culture (e.g., "if this statement were false, then ...").
What most people seem to fail to realize is just how different people are from each other cognitively, and how many different ways there are of getting to a particular conclusion. "Intelligence" is like a country's GDP -- a complicated, non-stationary mess that, taken together and measured in a way our culture deems important, ends up representing our "Gross Cognitive Product".
So, dual n-back probably improves working memory in most people, which will probably improve their problem solving ability, most of the time. But there are, without a doubt, many other subtle, complicated, and idiosyncratic aspects of cognition that are likely to have far more dramatic effects if appropriately tweaked.