No. As long as you have at least one licensed Zoom administrator account you can add and manage as many Basic (free) users as you want.
For example, you may want to buy Zoom licenses for all of your teachers, so that they can get access to all of the features they need, but only provide free accounts to your students.
What is the difference between a basic and a licensed Zoom user?
Basic users — usually student accounts — can host meetings with up to 100 others but meetings are limited to just 40 minutes. Currently this time limit has been temporarily removed.
Basics users also cannot user account add-ons such as large meetings, webinars, audio conferencing, or conference room connectors.
Licensed users — usually teacher accounts — are paid accounts that can host meetings of unlimited length. By default, they can host meetings with up to 100 participants and large meeting licenses are available for additional capacity.