Yes, you can write your own user registration, write a form that gets user details and use wp_create_user to create it.
That said, I think email verification is even more important on eCommerce sites, but if you willing to give up the advantages it gives to you and the users, then why not to bypass the whole user registration thing?
Another option is to use SSO provider like facebook and google to make the user creation process faster (you basically rely on them to supply you the current email address of the user).