If I copy the response information onto a spreadsheet and delete the names that are stored on my form, will it continue to take responses for me?
Yes, just be careful with the 50 for the free account. If you forget to export and hit 50 responses then the next person to fill out the form won't be able to submit. I usually suggest people who are actively receiving responses to have at least a Basic account.
This FAQ may also provide some insight - it explains how the Plus limit works: