Will customers receive abandoned cart emails even after having placed an order?

No, if you have a series of multiple abandoned cart emails setup - let's say at 1 hour, 48 hours, and 7 days - if the customer completes the purchase after receiving the first abandoned cart reminder, then they won't receive the second or third.

Also, and this is an important use case, even if the customer calls in to complete the order over the phone (which technically creates a completely separate quote in the Magento database), that order will be recognized based off of their email address and they won't receive further abandoned cart emails.

The only exception to this is if there are certain order states where you actually want the customer to continue to receive abandoned cart emails. For example, in some cases, merchants have payment methods setup in such a way that an order will be created in a "pending payment" state and the customer still needs to finish their order.