Is this an acceptable way to support an undermount sink?
I have to say that those scrap pieces of wood look like rather shabby workmanship to me. I would definitely have the installers come back out and clean up that mess.

If you have any chance to hold up any due payments you should do so until this is corrected. 

I cannot say whether this is an overall acceptable way to support the sink but if it is expected that some support piece is to be attached to the cabinet there are surely neater ways to achieve this than a couple of splitting 1x2's stuck in there with drywall screws.