Screwing 2x6's to the face of your 2x4 walls create 'ledger boards' like attaching a deck to the side of your house, however that deck attachment is different and has to be lag bolted through into framing members.
Ledger boards like you are describing would not be load bearing as there is no support under them to transfer the load down. Leger boards done in a way to pass code would then require the new floor joists to be installed with joist hangers.
Opening up the drywall and setting the floor joists on top of the walls 'top plate' to create a load bearing walls if the configuration of how the house was built would provide for doing so would be better.
About passing inspection - there are two kinds of inspections - home inspectors and building inspector from the local building department . Likely just about anything you do will likely get by a home inspector, a building inspector will be different, you have to apply for a permit with the building dept, pass the inspections and then there is nothing to talk about with a home inspector as the building permit superscedes anything a home inspector can come up with .