From a user point: no, you're always installing applications using the store which will be accessed using your Live ID. So to download the applications zune or your phone (you can install apps using the store app) you need to be online. The policy you can only install applications using the store was a decision for stability and security. Allowing to install applications bypassing the store as a security gateway opens doors for malware and instability (which will most definitely fall back on the platform itself).
From a developer point: You can developer unlock your phone and install the application using Visual Studio by debugging on the device. This is not a normal install and will legally work only with application you own (have access to the source code). To unlock your phone you need to have a valid developer account for Windows Phone.
There is a third option by jailbreaking (iOS jargon, not sure if it's called the same on WP). I'Ve never done that, it always seemed ridiculous to me to fiddle with one of my main communication assets (and maybe break it), so I wouldn't recommend trying.