Heavy pruning of Olive Trees

I have a few olive trees that are in front of my house that should provide privacy for my front room. I've allowed them to grow far too tall so need a lot of pruning. They are about 8 years old. The problem is I want to prune them to a much lower height so new branches and leaves will form to provide the privacy I'm looking for. If I prune them to the height I want one or two of them would just be left as trunks/stumps with no branches or leaves. Can an olive tree survive and then thrive, producing new growth from the stump, after that treatment? Is this a good time of year to be doing that? Thanks!