pfons, you must be even older than me!!
'Priming' is a throwback to very old engine preservation techniques, where bearings and cylinder linings were much less robust than in today's motors, and mineral oils did not have the viscosity range of modern synthetics.
I'm not saying you shouldn't do it, just that it is quite redundant for modern car engines. I'd also check what other systems run when prime cranking as you've described it. It is possible some of these should not do so without ignition/start-up.