hey Marie,
Cart abandonment follow-up is predicated on the business having the customers email. If the customer doesn't have an account, and abandons their first transaction, you really have no way of contacting them..
Secondlayer may be handy for you because it can ask any shopper a question (account or no account), or ask for their email address after they've been in your cart for a specific amount of time (say.. 30 seconds). This way you can get insight as to why they're debating making a purchase, or you can get their email to follow-up, and do some re-marketing.
Totally free for 14 days. Hope you give it a whirl..