Not really, 'quench' refers to thirst, so it works for 'desire' (which is a kind of thirst), but not for 'dream'. How about an 'unfulfilled dream'?

It's not a common, comfortable, or idiomatic expression. Note that in addition to quenching thirst, you can also quench a fire. Quenching a fire means to put it out by throwing cold water on it. Reading over the definitions at m-w.com, all of the meanings of "quench" carry the sense of sudden destruction. The word "dream" can mean a daydream or an idea. And there is an idiomatic expression, "to throw cold water" on an idea. If it is clear that 1) someone has a particular "dream" that is clearly, in some way, hot, burning, or fiery, and 2) people have trying unsuccessfully to "throw cold water on it" but the dream continues to burn... ...I guess you can speak of an "unquenched dream." Google indexes bad English as well as good, so you have to be careful... but Google actually does find some reasonable examples of the phrase "unquenched dream."