No. The cloud version is a paid service. However, Teclib' offers a 30-day free trial. During the trial, they automatically provide a temporary registration key. After 30 days, you must pay or export your data to the community version.
Before diving into keys and licenses, it helps to understand what GLPI actually is.
For over a decade, GLPI has been the go-to alternative for expensive ITSM tools like ServiceNow or Jira Service Management because it is entirely free via self-hosting.