You should be able to import as normal, even without an internet connection. It would just mean that the imported files can't be uploaded to the cloud until the connection is restored, which in turn means you don't have a backup of them, so if importing from a camera card it's best not to reformat the card until the upload has eventually completed.
Which app are you using? The Lightroom desktop app, or the Lightroom mobile app (if Mobile, which device type and operating system). I verified Lightroom mobile would import normally when the device was offline.