On any account application form, I would assume that there will be a question asking if you have ever been made bankrupt. If the person chose to answer no, I am fairly sure that the bank would take this on face value (on the assumption that there is no adverse credit in this country).
But of course that would be fraud!
As far as I am aware, banks do not cross borders very easily, and if someone is bankrupt in America, there is no way the banks here can tell.
Of course, if they have only just moved here and are not on voter's role etc, only basic account facilities will be granted anyway.