I don't think that the Mac Mini will have more problems to do this than any other computer, furthermore when it will be dedicated only to that specific task. Sure, every computer, even a server, benefits when you shut it down from time to time. Apart from that, I can't see any problem.
The two major issues that you may have (more likely) are the overheating of the power supply or the graphic card. But if it is not too hard to replace those, you should be good to go.
Having said this, I confess that I don't own a Mac Mini myself and I only know its generic specifications.