To answer the OPs question:
Ty for the response
November 5th Red Wings 4 Oilers 0 - Draisaitl, Maroon
December 10th Maple Leafs 1 Oilers 0 - Puljujarvi, Lucic
December 14th Predators 4 Oilers 0 -Puljujarvi, Lucic
December 31st Jets 5 Oilers 0 - Draisaitl, Maroon
January 2nd Kings 5 Oilers 0 - Puljujarvi, Maroon
January 23rd Sabres 5 Oilers 0 - Maroon, Caggiula (and Slepyshev)
February 17 Coyotes 1 Oilers 0 - Maroon, Draisaitl (and Slepyshev)
March 13 Flames 1 Oilers 0 - RNH, Aberg
April 2nd Wild 3 Oilers 0 - Draisaitl, Rattie
4 out of 9 games the Oilers have been shut out Draisaitl has lined up with McDavid as one of his two most common linemates (the Coyotes game both he and Slepysev played about the same amount but we'll count it anyway).
So 44% of the time the Oilers have been shut out McDavid and Draisaitl have been on a line together for a significant amount of the game.
But, McDavid has played 40% of his 5v5 time this season with Draisaitl (that includes the fact that Draisaitl missed 4 games). Drai has spent 45% of his 5v5 time with McDavid.
The Oilers aren't any more likely to get shutout with Drai and McDavid together than with them apart.