Yes, you can. You can use the arrow keys or WASD to move and the mouse to look around. You can definitely do both at the same time. Make sure you click on the game window to make the mouse disappear and allow you to control the game.
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The WebGL build seems to glitch a lot with the mouse hiding. You ought to just be able to click and it should go away, but I've found I have to have my mouse over the center of the screen while it is loading, then click when it "logs in". Try that? Sorry I would try to fix it but it doesn't have that problem in the Unity editor. I'll look into it.