Can DNA test of my grandparent's brother reveal my heritage from that branch of the family?
As Rayoub's answer points, you are likely to share a random part of your genes with your grandparent's brother, and therefore analysing his DNA won't tell you where all your genes come from, since he has some genes you don't have and you have some genes he doesn't have.

However, I understand that you aren't that interested on your particular genes, but on what genetics can tell you on the history of your family - that is, to shed light on who were your ancestors and where they came from. Then, if your grandparent's brother was your grandparent's full brother, his ancestors are your grandparent's ancestors and therefore analysing his DNA can be as useful as analysing your grandparent's DNA.

In addition, since your grandparent and his brother doesn't share all the same DNA (likely just about 50% for full brothers) and each of them just have a 50% of each of their grandparent's DNA, if you could analyse DNA from both a grandparent and one or more siblings, you would be able to gather more information. In fact, you would be getting closer to get the same information you could have got from analysing your grandgrandparents'DNA.