Yes, you can, by creating a workflow rule that executes a field update. 

How To: Create a Workflow Rule using the following criteria on the Lead Object

STEP 1: Add "Webinar Registrant" as a picklist option on the field "Lead Source"

STEP 2: Go to Setup > Workflow Rules > New to Write a rule using this criteria on the Lead Object. 

Registrant Key NOT EQUAL TO ______________________ (leave this field blank)

STEP 3: Create your workflow Action:  "Field Update"

If you are creating this workflow rule after you've already sync'd numerous Lead records from our GoToWebinar Integration, you run a report  that uses the filter "Registrant Key" " not equal to "_________". Add the column that exposes the Salesforce Lead ID and Lead Source field. Run the report, then Export to a .CSV.  Once you've downloaded the report, update the Lead Source field to to "Webinar Registrant. NEXT, perform Import, "Update"on the Lead Object.