Well, the simple answer is "it all depends".
Like any phone system, it all depends on the initial provisioning and install, their experience and/or incompetency, and how well they will support it/you. If they don't do all 3 correctly, you will have issues. So as with anything, do your own due diligence, get references, check them out thoroughly, and make sure they are on the level for what their salesman says they are.
Now since you didn't specify whose asterisk I can only assume you are referring to vanilla asterisk that you can download form
www.asterisk.org. As far as mission critical applications go I design call centers from 15 to 800 seats dialing upwards of 12:1 with some operating 24/7. I am not sure if a business exists that is any more reliant upon it's phone system then that.
The term "large company" could really mean anything. Since I could go into a 3-page long speculative essay on what Asterisk is and isn't, I think the better response is to ask "what are you trying to use it for?"
The biggest misconception I run into is that people believe that by just downloading and installing Asterisk will yield a phone system. In reality, just installing asterisk will yield nothing. You must tell Asterisk to do everything, including answer the phones. There is also a whole methodology to the things that go around it (servers, network, Linux distro's, Phones, etc) that are usually only picked up through experience.
Now I'm not trying to scare you away from using it, but instead trying to convey the point that it's not the end all solution for everyone. If anything I am actually trying to talk you into learning it. Once you get through the learning curve it can quite literally be anything you want it to be. However, this learning curve is what kills most people.
So after all that, is it as clear as mud or what?
