As mentioned above, the Revit Importer will only import what is visible in the selected 3D view.
The Revit importer selects which view is imported with the below process:
(1) Selects the “Starting View” in Revit if it is a 3D View and if it contains visible elements
(2) If (1) fails, Selects a 3D view that contains visible elements and that includes {3D} or {3D in its name. The view must have visible elements
(3) If (2) fails, Selects the first 3D view if any and if it contains visible elements
(4) If (3) fails, Creates a default 3D view
(5) If (4) fails, Returns an error
(This sequence of steps comes from @Jacques)
So I think the easiest way to control this would be to set the starting view (the view that opens when you open the project) to one specific 3D view that you are using to control what is visible and therefore what is imported. You can also set the starting view to be “Last Viewed” and then the starting view will just be the view you have open when you last saved the model. To set the starting view you go to Manage Tab>Manage Project Panel>Starting View Button.
Keep in mind that if this is a workshare model then whatever you set as the starting view will be what everyone sees when they first open the model. So you may want to either change the starting view back to what it was previously, after you are done using the Revit Importer or open a detached model and then you do not have to worry about that.
I believe in step (2) the Revit importer first looks for {3D} and if that is not there it looks for any view with “{3D”. So a potential workflow for using a workshare model that you do not want to detach or change the starting view on would be to use {3D} as the view that you always manage what is imported with the Revit Importer. If the {3D} view is deleted and you want to get it back into the Revit model without deleting all 3D views out of the model (you may want to do this if someone has set up rendering or presentation 3d views that you do not want to lose) you can do so by opening a detached model and then going to View Tab>Create Panel>3D View>Default 3D View. This will add the {3D} view back into the model but you would need to then replace the current workshare model with this one and tell people not to delete {3D}.
If you wanted to actually work with phases in SketchUp with an imported model (so be able to toggle between existing, demo and new) then I think the workflow would be to set up the Revit view that you are using to manage what is imported into SketchUp and then make only the existing elements visible (minus the elements that will be demoed) then save in Revit then import into SketchUp. Then do the same for the demoed elements and then for the new elements. The importer brings in each import as a component so you can then easily make tags and tag each component/phase as “existing” “demo” and “new”