I am considering buying a Kohler K-10579 bathroom faucet. Pictures of the faucet online all show the faucet with the handles in the up position, and I assume that is the off position. So my question is, in a faucet of this type, can the handles be configured to be OFF when they are down, and ON when they are up? Thanks!

Would depend on how the cartridges are configured. Some Delta cartridges can be swapped so the handles do change position from the supplied version. Unfortunately, you may have to buy it before trying a conversion. You can try calling Kohler. This model is a bit strange looking.