Hi, thanks for posting.
Right now, there is nothing in NCrunch that integrates with CoW in any way. That doesn't mean it isn't used though, as I expect the platform probably makes use of it quite a bit internally.
When NCrunch builds workspaces, it does so using File.Copy. In theory, this provides an opportunity for the platform to use CoW to help optimise. In practice, this is subject to the rules of the platform and results may vary. I would expect that many of the activities of MSBuild are engineered the same way (unless they changed since I last checked), so yes, there is room for the platform to improve NCrunch performance significantly, but I can't tell you how much, or make any promises on it.
The running of analyzers is controlled by the NCrunch config setting 'Allow code analysis'. As you've assumed, internally, this uses the RunAnalyzers build property. The config setting is set to False by default, so if you change nothing, you won't get analyzers.