Local storage Lightroom CC

Yes, if you're offline and you have stored the smart previews locally, Lightroom will use those SPs for editing.

When you say that you "deleted them from the hard drive completely", what exactly did you delete? When you import existing images from a hard drive, Lightroom makes a local copy of all those images and it is this local copy that is uploaded to the cloud. Depending upon other settings, that local copy will become eligible for automatic deletion (once the upload is complete), but the timing of that deletion will depend on various factors. So it is certainly possible (even likely) that some or all of that local copy is still inside the Lightroom local library, which explains why you can currently edit those images even when your system is offline. 

Originals and edit settings are stored in the cloud. Proxies are pushed to computers and devices as required. This optimises disk space and why you can delete originals from the library file without waiting for automatic deletion.