My powerline adapters are on the same phase. in fact, they are even on the same circuit just opposite sides of the room. My powerline adapters are located in probably the best condition ever. They are on the same electrical wire, probably 35 feet long and still I'm only getting half their rated speed. When I tried having the network connected adapter across the house, I was getting less than 250 Mbps on a good day. I never considered that they could have been on opposite phases. At one time I had up to 4 powerline adapters running but the speeds were just too slow and intermittent so I switched to MOCA where I could.
I see that you can get a pair of the ones I have on Amazon for $23. You could pick them up, try them, and if they don't work, send them back.