Hi lizdb,
You are absolutely right but Boaz is a very unusual name and I have accounted for every Boaz on the IGI, Familysearch, Ancestry, Rootsweb Worldconnect, FreeBMD etc.
With Joseph being from Somerset with a brother named Boaz, marrying in West Bromwich, living in Wigan with a living daughter recorded on the 1851 census but no sign of Boaz, it's a reasonable bet that this is the correct family.
If Boaz James was a man I would expect more evidence of his existence and there does not appear to be any.
Best wishes
rcuser