Short answer: It should not, probably.
Part One: The Hardware
What happens when you Hibernate is that your computer takes a capture of your RAM (Random Access Memory) which contains all the bits and bites your OS is using to show your programs. It save this and VM (Virtual Memory) on a dedicated space on your computer hard drive and then close everything. The main reason why it saves both of those is that at closing, both RAM and VM gets flushed, RAM gets flushed because if there is no power in it, it does't retain memory, and VM is flushed by the OS. Your OS use both of those to store al your applications while it present them to you and you interact with them.
So, hardware speaking, when you hibernate, the whole hardware get closed, so it would not affect it. The hardware sees it as a regular close.
The bit of problem you might have comes from elsewhere:
Part Two: The Software
As I said in Part One, when your computer run, the OS store all your applications in RAM and use that to interact with it. You know that step one of troubleshooting is restart your computer right? Well, the reason is there. If you run a lot of application for a long time, they get sometime messed up, sometime the OS get messed up with memory management and sometime bits of applications get stuck in the RAM. Over time, that cause clunky-ness and non-working program. So guess what happens when every time you reopen your computer, instead of starting anew with clean memory to deal with, it comes back to the mess it was... well, it creates more mess. You shouldn't see anything for the first 3-4 days. If you run Mac OSX, you can stay on nearly a week or two. But at sometimes or another, you'll need to restart your computer to at least clean the RAM.
And let's not forget, your computer will most of the time updates itself only by restarting, it won't do it in hibernation.
So, for the long answer: It can be a bit tricky to deal with but shouldn't physically damage your computer. All it will do is damage your mental status.
Edit: as someone pointed out down there, lets not forget that storing both RAM and VM on your HDD will take up place, with windows it normally goes around 9-12 Gig. And it won't magically clear itself when you wakeup, the OS allocate the place to reuse it afterward. So if you are short on disk capacity, take care of Hibernate