The offline restrictions apply to all pages you can navigate to from the offline profile. We have an app in which we plan activities (online, making full use of microflows and other online capabilities) and execute field work (offline, since the field workers operate in low-to-no-connectivity areas). The offline landingpage shows only this field worker part.
The modeler will automatically do consistency check if you're not using 'online' functionality on 'offline' pages.
As far as I know, you'll have to make a page that is offline only that syncs when the app comes back online.
I'm also investigating the possibilities for offline with Mendix as a part of my internship at Mansystems. As Hunter correctly states there is no option for both online and offline, so for example microflows won't work in a offline profile.
You can however for example use Administration module that uses the responsive browser profile, here you can use microflows and other online capabilities as Pieter notes.
And when switching to the application on your mobile it uses the offline profile and uses the offline pages and nanoflows you modeled accordingly. I think this is what Pieter means with his comment and it is also what I am experiencing with my research and proof of concept preparation.
I hope this answers your question!