I own a home and carriage house in the back. They are on separate electrical boxes and pay separate in terms of utility bills. My questions is, are these connected in any type of way where if I setup a Powerline Ethernet Adapter at my home, is there a way for the carriage house to pick this up. Are the electrical boxes tied together in anyway at all? Is there a way to find out?
They are tied together - they both share power from the grid.
Whether this will work depends on rather a large number of things, but particularly the sensitivity of the gear you choose and if they are on the same phase.
If it works, its unlikely to work well, but the only way to see if it works at all is to try it.
(Powerline networking is very similar to WIFI, only it uses the power cable rather then air as a wave guide. Things like meter boxes and RCD's typically interfere somewhat with the signal)