It is not possible to complete checkout without having an account created.
However, if you are using Paypal Express Checkout or something else that offers "checkout without account", the customer can avoid signing up manually. Their account is created in the background when Paypal sends back the confirmation, and it may be possible that you won't get some of the information you would like to collect.
What checkout options do you have enabled?
There is in admin > Configuration > Customer Details >
Customer Shop Status - View Shop and Prices
Customer must be approved to shop
0= Not required
1= Must login to browse
2= May browse but no prices unless logged in
3= Showroom Only
Also another similar setting under another tab, which I will have to look some more to find...



