Yes but remember you are also using that info for your own security (credit card fraud etc.) but what is making evrytning mandatory is if statements. You will need to take them off the parts you no longer want mandatory.
Anyway the differnce is that when you allow anonymous the user DOES NOT have to create a unique login. So you will get instead of a user lildawg I will be anonymous1 and the next user would be anonymous2 and so on. When you do not allow anonymous you will then have each user have a unique login name like "lildawg or funnytshirts".
To see what files are included in checkout just switch to webmaster mode and the go to your register page and you will see all the .tpl files that make up that page.
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