She may be fine and be permitted entry to the UK as a visitor with her second US passport, but I still think it's a very risky gamble.
As you cannot have 2 visa applications lodged at the same time, my worry is that to grant the visitor visa (which while less formal than applying for a settlement visa, is still an in-person visa application at the port of entry), the settlement visa application will be considered withdrawn and superseded by this newer visit visa application. Or conversely, because a settlement visa application is in progress, UKVI won't consider a request for a visitor visa and refuse her entry.