IIRC, Robert April was captain of the Enterprise before Pike. So he should be older, a higher rank, and a gold shirt. He also wouldn't be a member of the crew. Those are the issues I have. That said, April is an obscure enough character in Trek that I could bite off on this being his kid, Robert April II, or someone else with the same name.
It's the same April that captained the Enterprise before. Pike was his First Officer
Yeah, I suspect his presence may simply be one of "passing the sword of command" and possibly one of using the Enterprise to briefly get him from "point A" to "point B" for some kind of diplomatic mission. I highly doubt he will be a permanent part of the crew. His presence could possibly undermine Pike's authority on the ship, particularly since (theoretically) April was her first captain.April's not a member of the crew in 2259. He's an Admiral who meets with Pike on the orbital habitat over Jupiter. He's just appearing in the new series, not an Enterprise crew member.