No, but using version control is strongly advised for any embedded development project. It is especially important with an MPLAB Harmony project because the MPLAB Harmony Configurator (MHC) generates code which is merged with the user's existing project. Done right, this merge won't adversely affect the user project, but if mistakes are made in the merge, it can be hard to recover without version control.
The level of version control used depends on the needs of the user. Users who modify the underlying framework or board support package (bsp) may want to place the whole Harmony installation under version control. Users who only have modifications to their project under the apps folder may only need to place their project (apps/myproject) under version control, as long as they remember which version of Harmony corresponds to their source.
If you really don't want to use a version control system, the local history built into the MPLAB X IDE may be able to help.