I really doubt they would have gone abroad merely to get married. When the child was registered the mother, or even father, wouldn't have had to provide any sort of proof that they were legally married.
At the time Edward's first wife died there were small children to be looked after and it's quite possible Mary Elizabeth came to help out (or possibly even before that to help her pregnant or dying sister) and eventually (either falling love or on a more practical basis) became a couple. Possibly wouldn't do any harm to check for a marriage on GRONI as late as possible just in case.
