Saturation point of a CT is completely dependent on the particular design (i.e. core size, core material, number of turns).
DC offset can cause saturation.
If the primary current is pure DC, then no transformation occurs and there is no risk for damage.
If the primary current is AC with a DC offset or components, then saturation can occur. As a very general statement, metering core heat losses are normally pretty low and operation in saturation for certain periods of time will likely not cause damage.