I guess you mean RippleLabs... yes, the client code is just hosted on ripple.com for convenience, you can run your own rippled to connect to and set up a webserver with the client locally too (it's what I do for example), I linked the repositories before. I'd recommend to use the tagged release versions and not bleeding edge code as it is under active development.
So if I set up a centralized webserver as you suggest, the trades will be distributed with the Ripple Labs hosted transactions?
rippled is not a webserver, you would probably deploy ripple-client on a local webserver though. Then tell the client to connect to your local server instead of the official public servers and your local rippled server needs connectivity to other rippled servers of course (just like bitcoind). I am not sure what you mean by "Ripple Labs hosted transactions".