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NP - I leave my ceiling light on in my studio all the time now. If you set your camera to say... ISO100, F8 & 1/160th and snap a shot without your strobes going off, unless your ambient light is EXTREMELY bright (unlikely), the picture will come out completely black (extremely underexposed).
This way you know there's no real impact on the photo's from the ambient when the strobes do fire. I do this to keep pupils from getting dilated and to help focus in an otherwise dim studio.
All and all, a bit of ambient doesn't impact the photo in any negative way at all, but helps in several.