Bit ambiguous really. Memorising opening moves doesn't necessarily benefit you that much but understanding opening play is much more important especially at our level. I have been up to about 1350 in blitz but i reckon you could get much much higher than that without knowing opening lines. But understanding the prospects of certain openings and how to defend against them is important.
Might be wrong someone higher rated will comment surely.
How high in rating can be achieved without knowing any off chess openings but just the principles: try to dominate the centre of the board and protect pieces but give them space to move etc...? What is your rough estimate and opinion?