Having enough Cloud storage is a must, clholt. Not having enough space wouldn't affect your phone in any way. It may mean that if you have photos, videos, or other content that isn't backed up and ran into a situation where you were to lose those items, they would not be recoverable.
Follow us on Twitter @VZWSupport
If my response answered your question please click the 'Correct Answer' button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!