We have just moved into a mid 1950's home which was wired with a 2 wire circuit--NO GROUND. I have purchased an stand alone GFCI 5b Outlet Adapter for protection(Tower - 5 Outlets, 125 Volt, 15 Amp, White, GFCI 5b Outlet Adapter 5-15P, 5-15R NEMA Configuration, cUL, UL File E174279 Mfr Part #: 30440003 MSC Part #: 36029262). My question is can I install a Model # DDT595SMJES 24 in. Top Control Dishwasher by GE with this GFCI outlet adapter substituting for the Ground protection, or will the GFCI not protect from electrocution if it has no ground? OR, is this GFCI Outlet Adapter going to serve the same function os a 3 wire grounded circuit with a GFCI?
Looks like cheese junk from a brand no one's heard of. You certainly shouldn't use random stuff that fell off a truck in Shenzhen for life safety.
It's also too expensive for what it is. Cheaper would be a GFCI breaker from top makers like Eaton, GE, Siemens, etc. Cheaper still would be a GFCI receptacle from a decent maker.
In any case, the device has a 5-15 plug, which means it's not listed to use on an ungrounded receptacle, if it's listed at all, which I doubt. Which means either a) it won't plug into your receptacle; b) you have a 5-15 receptacle that is illegally installed with no ground, c) you have a GFCI receptacle legally installed without ground, or d) you have a 5-15 receptacle that does have a ground after all.
I would do option C and install your own GFCI receptacle or breaker, and call it done.
A GFCI is adequate for life safety, as it will stop electrocutions. Some equipment needs proper earthing for reasons not related to life safety, e.g. radios or recording studio equipment, a GFCI will not suffice for them.