If it's happy!

If you took the cutting from the tip of a cane that has already bloomed it should climb. Sometimes if the cutting is taken somewhere else it just becomes a rose bush.

A lot of climbers really need a rootstock to push the climbing growth. In a warm climate, they may eventually build up enough to climb. Since Joseph's Coat isn't the hardiest climber anyway, in a cold climate I wouldn't expect it to do much of anything.