Sorry
That's Incorrect

No. In fact a high error variance would work against
finding an effect for the independent variable. Think of it
this way; a high error variance means there is great variability
among the participants within each comparison group. Then,
in order to show a significant effect for the manipulation we
need an even higher variability between the groups. In essence,
the independent variable will need to have a far greater effect
in order to overcome the already-existing within-groups variability.