Permanently installed flooring, yes. Floating floors, no. But the cabinets all have to be shimmed to the finished floor height.

It isn't required, but I think it's a good idea. It can be cost saving, depending on the flooring material you are using, however, if you are ever planning on changing the cabinetry configuration, it can be a complete headache (and great expense) to try to patch the flooring to blend with the rest.

In my projects, I typically tell the contractors to run the floor under the cabinets, but it's really your preference!