Hi Benoit,
Because I didn't understand too much from your question "Would their not be a clever way to count the seconds I speak
with the timer0 of with the DS1307 RTC that is attached to the µC? " , I presume you are more concerned to the accuracy of the clock.
The DS1307 specification clearly stated as ±2 minutes/month at 25°C .
Choosen between DS1307 and delay done on timer 0 basis, it's dependent upon your application's requirement. Bear in mind that DS1307 RTC it's not a nice option due to lack of interrupt request feature, like DS12887 i.e.
You'll need to poll the DS1307 through SDA and SCL lines in the main program loop, in order to know when the time elapses. You can find an example here **broken link removed**
If you need timer activity even during power supply fail, DS1307 could be a good solution because has a built-in power sense circuit that detects power failures and automatically switches to the battery supply.
That won't be too easy to achieve using delay on timer 0 basis.