Yes., especially in your climate should survive winter and keep on growing.

I live in a semi~detached home in Ontario, Canada. Our neighbour plant Ivy a number of years ago. Last year this plant started coming through the fence, also, it is growing along the aluminium siding and along the eaves through. Yesterday I pulled all that I could reach off the wall. I then took a razor blade and scraped the "suckers" off the wall and ended up washing the entire back wall of our 2 story home. My questions is this: How do I prevent this from growing back on our side of the house?
Thank you.

Firstly, is it definitely Ivy? Hedera helix, common ivy, doesn't have suckers it has aerial rootlets. Suckers, ie little sticky pads, sounds more like a Parthenocissus of some sort eg Virginia Creeper or Boston Ivy. Ivy is evergreen, the Parthenocissus are deciduous.

You can't prevent it other than trimming it the minute it creeps onto your territory. Or you could try negotiating with the neighbour about removing the whole thing.