It will be all quads Dave. If you bevel with two segments it would be like manually putting a support edge on either side of the original edges with a little smoothing to boot.

The nice thing here is you don't really need to smooth afterwards and you get a very nice edges. But if you have to smooth it will work out as well and if you subd the 5-sided ngons of the main faces will be transformed into all quads.

Here is a quick video to demonstrate and you can see the corners are nicely quadrangulated....

https://youtu.be/kK3UT3eTPtg

PS - I did notice the main faces are indeed dreaded ngons (5 sides) but if you convert to subd the catmull-clark algorithm will convert them all to quads.