sometimes i find big companies are using wordpress but i do not know if they use it just as CMS or they use plugins and Theme .
There are some feature rich plugins to set you up with booking systems in WordPress. Depending on your specific needs you might not have a lot of work to do.
There's nothing requiring your actual booking system to be managed by wordpress plug-ins. You can still have a look-and-feel designed in wordpress, but when it comes to functions of your booking system, you could have a completely separate hosted application. The advantage of Wordpress is that if you don't have a full-time web designer/programmer, you can get a lot of bang out of the WYSIWYG tool. Otherwise, as a programmer, I find it incredibly irritating to use, and I can never extend beyond the limits of what WP has decided to include.
You can do anything using the WordPress, what you need is better understanding of the system, themes, plugins, security etc. Sometimes it might not deliver the exact the same and require customization. If the required system is too big, probably it would be a good idea to develop a Proof of Concept using WordPress and slowly migrate in to proprietary.
Please allow me the audacity to say to you: You're asking the wrong question :-)
You don't build a BIG website, a website becomes big. As such, you start small with Wordpress and then you scale accordingly, with whatever platform fits your needs when the website is big.
Dimensioning a big load before hand, is one of the biggest waste in re$ources that an startup could do.
Best of lucks!
What do you mean by big? Big in terms of scope, load, users or the revenues? Start lean, get a proof of concept out, test the concept before making any decision. If your question is to replace an existing system with WordPress. Answer is "Yes" and "No".
You can, but why build it yourself - use something like BookingBug http://bookingbug.com - they have a huge range of offerings and have done the hard work for you. I'm not involved but do know the founder.