How do I set a case open date and/or close date with a webform?
I don't think so, no. But then, I don't think you can do this through the regular CiviCase UI either.

Perhaps the solution would be to expose the opened and closed dates to the webform as fields? This would require patching webform_civicrm/includes/utils.php to add them under function wf_crm_get_fields). If that works for you, please submit a pull-request back :)