Am I correct to assume that fitting the RainSava a little higher than
specified so that the connector is level with the 'flat indent' will cause
an overflow?

It depends on how far the water level rises up inside the device on the
downpipe, before diverting back down the pipe. Have a good look inside and
see how it works. Incidentally I had one of these at the last house and it
was a PITA. Leaves washed down the gutter would block the downpipe at the
point of the Rainsava. That line at the bottom of the fitting instructions
about removing it and washing out is vital.

Mike