TurboJ,
The student can indeed fly as P1 but they are still a student and must be authorised and it must be solo and it must be to and from licensed airfields unless a microlight.
What you talk about is common at most schools I know. In the majority of cases they do not charge for the solo supervision and the "student" gets the aircraft at the ppl hire rate. Prevents them going rusty while awaiting the paperwork.
---------------
18Greens,
Provided that it is a licensed airfield then there is no reason why you can not send the student solo if you are happy.
Regards,
DFC