Any damage done to the engine for a few seconds running with new oil in the case is minor. You can't get all the oil off the components when draining it anyway, so everything is coated before you start the engine. Just like any other cold start.
Neither would I bother to fill the oil filter can when changing oil - for the same reason. Use your time for other things.

There are far worse things one can do to an engine than starting it.

Wear down of engine parts comes from not changing the oil often enough. The build up of soot and other particulates in the oil age an engine pretty fast.

__________________
DS
2010 CL550 - Heaven help me but it's beautiful
87 300D a labor of love
11 GLK 350 So far, so good
08 E350 4matic, Love it.
99 E320 too rusted, sold
87 260E Donated to Newgate School
www.Newgateschool.org - check it out.
12 Ford Escape, sold, forgotten
87 300D, sold, what a mistake
06 Passat 2.0T, PITA, sold

Las Vegas NV