Maybe, but I don't think you necessarily need to. I started with A Deepness in the Sky and then read the other two (and then all the other books Vinge has written).

Especially since it is actually a prequel, I don't think the order is that important.

There are things in Deepness that will have more significance if you've read A Fire upon the Deep, but nothing central to the plot. They're both standalone novels, just in the same setting/universe/background.