Yes, but a colour control primarily adjusts lightness, with some effect on saturation. The more you adjust it, the greater the effect on saturation.
Getting lightness correct is far more important for the appearance of colour than getting saturation correct though. Of course it would be best if you could have both correct.
You can fix' it with RCP so that the colour points are on the Rec.709 gamut, but if I remember correctly, that completely threw off lightness.
I've been meaning to recalibrate my HW10 again recently, so I'll set it up with my i1Pro in an hour or two once it's warmed up.
EDIT: Are you using a colorimeter to calibrate the projector?
I'm getting quite different results with my i1Pro. Using no RCP:
I would normally use uv charts rather than xy, but used it for comparison here.