Ha ha! That would be fun to see
I've only ever heard two BoC songs on the radio here: once many years ago on an experimental music show on community radio (Music is Math). It was so weird hearing someone say "Boards of Canada" and "Geogaddi". Sad, but I'd never actually heard another person say those words before
And about two months ago I heard Roygbiv on student radio. It's quite an awesome feeling hearing music you love when you're not expecting it.
There's a discussion/debate programme on TV here called Insight - they've used BoC a few times over the years. Probably the oddest was on a show about last year's federal election - they played A Moment of Clarity over graphics of election opinion poll results. In 2002 or 2003 they played Melissa Juice in a story about evangelical churches - that shocked me!
Most recently I was surprised to hear the beginning of Sunshine Recorder on a skateboarding video.
EDIT: Some others that have come to mind:
There was a Lewis Black video that was a pisstake on crappy TV. I can't find it now (it was taken off YouTube) but it essentially was a bowl of celebrity faeces spinning around 24 hours a day and people would ring in and guess whose shit it was. He said it would have a "new-age soundtrack", which was Turquoise Hexagon Sun (though it was only heard for a second or two each time).
FashionTV shocked me once by playing Alpha and Omega many moons ago, and MTV Australia used a very short snippet from Slow This Bird Down for a sponsorship advertisement.
I'm not sure if these rank as "unusual". I wish I had more interesting examples though, like "this one time a police car went past playing Nlogax!! OMG!!"