In short, it will depend on what jobs you apply for. 

You can complete the NTI registration, assessment, and training process without needing any phone.  Some employers will require you to have a landline, though most accept 'softphones' that you can run on your computer, and will usually provide the software to do so.

If you receive a job offer that requires a landline, you may have to act quickly to obtain one, so it is a good idea to check ahead of time if lines are still available in your area.