Hi Beverley, when you import a list, the contacts aren't cookied in Marketo until they fill out a form, or click a link in an email that is sent to them via Marketo. Therefore, they can still be "anonymous" until they do any of these actions, but as long as the email address that they complete this action with is the same as what you're importing, then they will be cookied -- and their anonymous activity from before will also be linked to them.
For this reason, when a list import is done, it is best to try to get them to click a link in an email, so that you can then begin to connect their history to the record.