Yes. On Legalesign there are numerous email options to cover almost every conceivable circumstance.
An admin user will need to set the team default, or custom signer experiences for different situations. Go to Admin > Signing experience > Email options and tick the tick box labelled ‘Attached PDF to first signer email and reminder’. Save changes before leaving the page.
To learn about other email and pdf attachment situations review these links: all signed documents for the team can be CC'd to one or more emails, you can associate a 'reviewer' with a particular signer to received a CC copy, or export out all signed docs to Sharepoint.