Janie,
No, you do not need to uninstall ArcSDE 10.0 to upgrade the existing sde 10.0 gdb to 10.1. As the upgrade is done using ArcGIS Desktop, the ArcSDE s/w plays no role in the upgrade here.
However, I would suggest that once all the sde GDBs are upgraded to 10.1, you should install ArcSDE 10.1 as well. It helps to have all the softwares at the same version.
Regards,