While Morae may run under Parallels, it is not recommended. Parallels has a maximum of 32MB of emulated Video RAM and since Morae minimum hardware requirements state that 64MB of video RAM is required (128MB Recommended), it is not recommended that you run Morae under this environment.
This causes very poor performance with multimedia applications and is not reliable.
If you are looking for a solution to run Morae on Mac hardware, please try BootCamp.
BootCamp is included with OS X 10.5 Leopard and later. BootCamp runs Windows natively, not in virtualization, so it can utilize all of your system resources, where with Parallels, system resources are shared with OS X.