Do the Quincy know of the consequences of their power? We know that when a Quincy kills a Hollow, they destroy its soul and cause an imbalance that could destroy Soul Society and the material world if done enough.

Are the Quincy aware of this fact? If so, why do they persist in killing Hollows?
They were acutely aware of this fact.  From the Bleach Wiki, emphasis mine:


  Since the origin of the Quincy, many years passed within Soul Society trying to appeal to the Quincy that the handling of Hollows should be left to the Shinigami. The Quincy refused to accept the situation. As time went on, the number of Quincy increased and the cycle of souls became more unstable, forcing the Shinigami to reluctantly wipe out the Quincy in order to maintain the balance of the world.


From this, I gather:


The Quincy may not have originally been aware of what their powers were doing.
They learned the true consequences after the Soul Reapers attempted some kind of negotiations with them to get them to leave Hollows to them.
They disregarded the consequences and continued to use their powers against Hollows, due to (often) slow responses from Soul Reapers.