short-sleeve button down is what I’d call that shirt…and, !YIKES! is that link an ugly shirt!
Not button down.
Brainiac has a very nice one with tiki drinks embroderied on it. You really can’t go wrong at an office function in a shirt with tiki drinks. 
It doesn’t work with a light suit. If you had a charcoal grey pinstripe (or other dark suit) you could do a black T shirt, but a better choice would be a collared 3 button knit. I wear a dark grey suit with a black 3 button knit shirt and it looks really cool and get many compliments by those who would be highly critical of an International Male of Miami Vice look.
T-Shirt: TACKY! TACKY! TACKY! May the fashion police beat you to death with Martha Stewart.
Polo Shirt: Nearly as tacky, but your punishment would only be to be beaten to death with a picture of Martha Stewart.
Turtleneck: Can work, but only if done carefully. In general, a dark turtleneck works better than a light turtleneck. A light turtleneck screams “Shallow Art Show Cheese Nibbler” while a dark one looks more scholarly.
Ah I should clarify. The three button knit I’m speaking of is NOT a polo shirt. More something like this, but with buttons and no detailing:
My second choice would be a mock turtleneck, but definitely not a full turtleneck.
I guess I am going to have to find a way to post the photos of the event…and let the fashion police have at me.
I think the context also has a lot to do with it. This is Southern California. We’re pretty casual and “anything goes”. The look might not play as well in other formal or conservative areas.
ok…
here’s a chopped off pic of the suit and shirt…
I think it’s enough of a view to get the fashion polizei to vote yes or no…
Yep, that’s what Brainac4 does. I think it looks fine.