Dude... you had a hole in the pocket ;-) (Good ol Beatle's joke)

I tried it... no way without triangulating ( Looks ugly, not nice to model )

But.... :attn:

Do you know Subdivisions on Polygon Objects?

Look at the screenshot. You need edges at the front after your bool - and you can't insert edges after the bool because of the "Cannot start up a hole"-issue

So... you have to raise the Subdivisions on your base object so the bool has some "food".

My english is bad today, i think the screenshot tells it all.