Did the Bank War divide the North and South economically?

I would say that the Bank War (I'm assuming you're talking
about Andrew Jackson and his "war" against the Bank of the United States) did not do
anything to divide the North and the South.  This was a battle that was waged on
ideological and to some extent economic grounds, not sectional
ones.

In general, Jackson had the support of most of the
"common people" of the US (whether North or South) in his fight against the bank.  It
was a populist issue where you had the "regular" people lined up against the elites. 
Because there are "regular" people and "elites" in every section of the country this was
not a sectional issue.  Instead, it was one where the regular people supported Jackson
and the more elite types supported the Bank.