No, it depends on the converter. There are converters that leave 160V on the DC power rail for a 110V AC input, and 155V on the DC "ground" rail.
They are economic and you could find then when galvanic isolation is at least in theory not important, but they're terribly unsafe when used on PCBs that people might muck with.
If you have some "normal" converters and some of this kind, sharing the ground would be quite dangerous.
I think a circuit should mostly care about the deltas, but when you’re talking about things like phone lines, the earth becomes part of your circuit. You can’t influence its potential (it’s almost exactly neutral because any charge imbalance gets removed by interaction with the interplanetary medium) so everything else is going to end up being determined by what you need for their relative potential to that.