Since A voiced Protagonist is a thing now, I've played several games where I could choose which voice My character had. Will Fallout 4 have a similar feature, or at least a Deeper/Lighter meter for voice options?

No, I'm certain there is only a single voice actor for each gender of the protagonist. It wouldn't be cost effective to record the same lines with multiple voice actors.

You are right. Todd Howard stated that there is only one voice actor for each gender of protagonist. Each recorded over 13,000 character lines over the course of 2 years.