Unless the entire blade is of nano thickness, the same issue applies.
If the blade is 1mm, 2mm or 4mm thick doesn't really matter if the edge in question is measured in nanometers. . . .it's still a "thickening beyond the leading edge" that would in many (but not all) cases prevent cleaving of hard/thick targets.
If indeed we're talking about a monowire (a chain of single molecules that form a "wire" blade sort of like a cheese knife or garotte) or a monoribbon (a one molecule thick strip of any width) then the issue wouldn't arise. . .but if the blade has any thickness at all, it wouldn't logically cleave the same way the wire or ribbon form would, due to binding. (as to if game mechanics would follow logic, I cannot say.)
Even making it a quazi-energy weapon akin to "A strong magnetic field holds the wire out rigid" or something similar, it's not really a form I would call a blade or edged weapon at all. . .it's a super sharp string or ribbon (about as close to 1 or 2 dimensional matter as you could get in a 3 dimensional world). Monowire seems more akin to a really nasty garrotte than a blade, or even really any conventional concept of a melee weapon. (How could you parry with it for instance?)