Can Poison Snakes Mate With Nonpoisonous Snakes?

First of all, the correct terms are venomous and non-venomous.  A "poison" is something you have to swallow or inhale in order for it to be harmful.  
But, no, venomous and non-venomous snake species cannot mate.  They are not even related to each other, have very different DNA, chromosome counts, courtship habits, and often, reproduction.  Most North American and European venomous snakes give birth to live young, while many non-venomous species lay eggs, so this would be like a dog mating with a chicken!