Unlucky not, you cannot, except you write your own internet browser.
If you have to do some tests you need a test machine, whatever is a virtual machine or a real one, so you have to ask your Unix admin (or hosting provider) how you can put in place a development environment.
You can also install a VM on your PC, install a Linux distribution, Apache and test your changes (it's not as hard as it sounds)
To better explain, each application is written using the standard libraries, this way nobody has to rewrite the low level library and functions like the gethostbyname().
These functions normally are set to use file (/etc/hosts) and DNS, so, unlucky, if you need that your browser will resolve a name than the one is set in the /etc/hosts you don't have too many alternatives.
- You can set up your own DNS server and ask who has root rights to change the /etc/resolve.conf
- You can install a proxy server like DeleGate and set some rules for your VirtualHost
- Ask sudo rights on that customer host
- Change the behavior of the application you are using to test the connection (I guess the browser), for example https://addons.mozilla.org/en-US/firefox/addon/switchhosts/