Ah Justin, it's tough to have to answer these questions!
Yesterday to the office I wore the Black version of these with a pencil stripe shirt (Black/Purple) and a black merino vest to break up the patterns. But I wouldn't have worn the shirt without the vest.
The general rule is to wear solids with the glen plaid, though that rule has been pretty much exploded when you look at mens dress fashion. Millar, Hilfiger, Lauren and others all have gone to checks with patterns and glen plaids. But there is always a solid with one major piece to anchor the whole look.
So..... I'd say you are safe with a pencil stripe shirt if you have a solid sweater/pullover on (with no plans to remove it). Otherwise stay with a solid shirt.
Back to you....