No. A single side is adequate.

What causes the change to occur when you touch the panel is that
oscillator current is flowing on the outside of the panel. The way to
avoid this is to completely enclose the oscillator with a shield.

Roy Lewallen, W7EL

-exray- wrote:
On an example like a simple homebrew 2 tube regen set it is typically
recommended to use a metal front panel to "shield" the ckt from hand
effects. However, you can still notice some effect by touching the
ground/panel.

Would one see any advantage by using double-sided PCB with the two sides
not electrically connected?

-Bill