I rode a 300K brevet recently using clips and straps to try them out. I had no difficulty with them. Messing with the straps is not as convenient as clipless pedals, but if your doing that very often, you're not making good time on the brevet!
Other than that, I've only seen two other cyclists ride a brevet in my area without using clipless pedals. Both of these cyclists had forgotten their cycling shoes and were making do.
I see brevet riders using MTB pedals as well as road pedals for clipless. I prefer SPDs because the shoes are more walkable at controls.
You should use whatever is most comfortable for you. Experiment with different combinations. And remember that cyclists have ridden many brevets with clips and straps.