For me, it depends on a number of factors. Like @JLeslie said, the terrain will affect how I approach the intersection. Also, if it’s one lane in each direction, or a three way intersection, I might go faster than some busy ones where it’s two or three lanes in each direction and more chaotic. If I’m turning right onto a road where those people are turning left onto the road I’m on, I will probably fly through the right because those people turning left are showing me that nothing is coming (which is how they’re enabled to turn left).
If there’s nobody else in front of me, I may hesitate but if I’m in a parade of cars and the green arrow is on, and everyone is flying through, then I’ll fly through in the parade, too.
If it’s a busy intersection or hilly terrain, will probably not come to a total stop, like I would at a stop sign, but yes, I may hesitate (may hesitate, not “will hesitate”) and not barrel through, if it’s a busy one. My point being that for me, there are no hard and fast rules as to when I may or may not hesitate, it depends on a bunch of things. I was out and about the past few days with lots of holiday traffic on busy local roads, and there were a few green arrows so now I’m thinking about the various types of intersections that I encountered.
A little caution is not a bad thing, especially when the majority of accidents on local roads occur at intersections.