No. 

Once your check is completed, the DBS will post the certificate to you. You cannot receive the certificate via email, or, electronically in any way. 

You will receive ONE paper copy of your certificate. You can request a further copy if you meet the criteria for a reprint.

You can sign up to the DBS Update Service. This is the closest you can get to having a digital version of a DBS. Once your check is completed you have 30 days to sign up. You can find more information here.