Turning-off Watchdog Timer
The purpose of the watch dog timer is to reset the MCU should a hardware or software fault occur. It does this by generating an interrupt at certain intervals and if the interrupt does not get serviced in a specified amount of time, resets the MCU.

In general, the result of a reset mid way through your program will depend on what exact hardware the MCU is controlling and what state it is in.

For the clock you are building, I wouldn't worry about this since any type of failure will not be critical. I would say feel free to disable the watch dog timer to save power but since this is not a hobby/diy project, discuss the impact of this with your client.