Absence of evidence is not evidence of absence; does that work with "God"?

If something is a localized phenomena, either a discrete organism or event, and we have no evidence for it, it still might exist in some place or time we haven't looked. But if something is supposed to be omnipresent, shouldn't we - by definition - be able to find it anywhere? Doesn't the "absence of evidence is not evidence of absence" claim fall apart here?