Your problem would be accuracy. The Arduino's crystal is 16MHz, not 16.00000000MHz. The problem is that the error will accumulate. That actual error will likely vary from crystal to crystal.
Having said that, I say go ahead! I assume this clock will have an interface, so you'll be learning to handle an interface as well as the arduino code. Even if you find later your accuracy is not what you wish, you've got your display already and you can just add a RTC (like the DS1307) to get the accuracy in line.
-j