If it's a magic effect, like silver weapons against werewolves, sure. But not if it's just a poison. Poison just isn't a very effective weapon in melee combat. The deadliest poisons in real life take several minutes to even show symptoms, while swordfights are over in seconds. All poisoning your sword does is let you turn a total defeat into a Pyrrhic victory. If you don't care about your life, all you have to do to be sure you kill your foe is to land a hit. Basically, poisoning your weapons doesn't do you any good if you care about your own survival. Either you win the fight, then you didn't need the poison; or if you lose the fight, you're dead. Your foe might die a few minutes/hours later, but that doesn't bring you back to life.
So with this in mind, is it really worth using a weapon so soft that just a few swings will bend it out of shape, and one or two hits on a hard surface will dull it?
If you have to use copper, switch to ranged weapons. Who cares if your arrowhead bends?