Mass-effect – What does the day one patch do for Mass Effect 3 on Xbox 360

According to Wikipedia, you will need an Origin account for both the single-player and the multiplayer campaigns in ME3.

Customers purchasing PC editions of the game (retail or digital) will be required to install Electronic Arts' content delivery and digital rights management system, Origin. The Origin client (and an Origin account) is required to install, activate and run Mass Effect 3 on a PC for single and multi-player portions of the game.

This Bioware forum post by Chris Priestly gives a lot more detail around Origin and Mass Effect. Specifically, it speaks to your question:

Is constant Origin connection required or is it a single one off authentication when the game is first installed. Is there also a limit to the number of installations available? Mass Effect 3 will require a one time, single authorization for the single player game. There is no limit to the number of installs. Playing Mass Effect 3 Multiplayer will require a constant connection.

I did some experimentation this evening before and after installing the game to the hard drive:

• Loading to title: unchanged. Both times it took about 54 seconds to get to the main menu.
• Loading a save from the main menu: 8 seconds (25%) faster when installed.
• Reloading the same save: 2 seconds (10%) faster when installed.
• Elevators in the Citadel: 5 seconds (25%) faster when installed.

You're not going to save a heck of a lot of time per-load, but if you plan to invest a good amount of time in the game, it's probably worth it to install to the disk.