Not so! That just depends on how long you dive and how much drag your plane has. And if the plane stops accelerating faster than 9.81 m/s² the fuel WILL fall forward. That happens faster than you think... unless you have a really fast plane, and keep the power on during the dive... and then still...
The only things keeping your engine from running out of fuel are the facts that it uses very little fuel at idle and that most dives don't take very long.

Any square, rectangular or cylindrical fuel tank has enough space up front for the clunk...