Re: 2003 Selespeed Auto (citymode)
Yes, insurance companies classify the Sele as an Auto so that's what it is legally.
The City mode can be a little jerky and not as smooth as a standard auto because it has the same type of clutch as a manual car, a dry plate, not a torque convertor. But this means the fuel consumption is less that a standard auto.
As DavidC says, your gf could actually change through the gears 'manually'. She will have a bit more fun and also, it may encourage her to go for a manual driving test in the fullness of time, not a bad thing.