Oh my gosh, of course it is! Who hasn't heard of a poor boy (middle-class boy?) having a crush on a gorgeous rich girl? As humans, I think it's in our nature to want what we can't have whether it be a love interest or "old money." If you want to boil this part of human nature down to a grand desire for "happiness," then all of us can truly relate to Dexter's life. He works his entire life to gain what he thinks will make him happy: Judy Jones.
The irony is that we are often wrong about what will make us happy! There's nothing more depressing than gaining what you desire and then still being miserable.
I think the way in which the themes of hopeless love and social advancement are presented in this excellent story make it clear that the troubles and hopes and ambitions that Dexter faces in this story are not just confined to the so-called Jazz Age of the Roaring Twenties in America. It is clear that these themes are timeless and universal, and could occur in any setting. The figure of femme fatale as personified in Judy Jones and the way that Dexter sacrifices everything to try and gain her is one that is echoed in many texts, and likewise we see that the theme of Dexter's rise to power and status is one that is common to many texts.
Part of the power of good literature, in my opinion, is the way in which it is universal. Although we are separated from the context of this excellent story by time and geography, we can still identify with Dexter's struggles, hopes and aspirations, and these themes resonate with our experience of life.