Wonder Woman has +1 to her stats via the utility belt as she pilots the Invisible Jet. Can the Jet replace its stats with Wonder Woman's modified stats?

While a character is off the map, it can't use any game effects (including Resources and Relics assigned to it), unless a special effect says otherwise.

In this case Wonder Woman would not be able to use the modifiers from the Utility Belt while she is a pilot. The vehicles trip effect for would only be able to replace it's values with the unmodified (printed) values on the current click Wonder Woman is on while she is off the map.