If you are only planning to use Wordpress for the bank's blogging or publishing functions, then it is doable. However, if you are planning to have it interact with database they use for their customers, payments and transactions, I do not think Wordpress alone is the right tool unless you have the programming skills to completely hack WordPress. If you have that level of programming skills, then you are probably better off coding a custom solution for your client. To do that, you might want to have a team with all the skills and experience required to cover all the expertise a bank website would typically require.
Do you have a different answer that might help the questioner? How would you answer this question?