Add rule for a webform checkbox to autosend email after specified time
You will also need Webform Rules, but once you can react to the submission, you should have no problem getting this going. You'll need to schedule the rule to run in the future and will probably need to add a Rules Component containing the actions to run at that time.

In your triggered rule that reacts to the Webform submission, you need a condition checking if that checkbox was checked and an action that runs the Rule Component you defined earlier. You will want to pass the user object to it (or uid, or email address, or Webform submission - whatever you need) to make sure it works correctly.

I am using Drupal 7 terminology here, but this is achievable in Drupal 6 as well. Just replace "Rule Components" with "rule sets."