I don't believe there is a specific conflict between the license manager and enterprise versions. There may be a conflict between ArcGIS Pro and Enterprise versions. For instance, 3.2 implemented new field data types (date/time). These are not compatible with enterprise geodatabases that haven't been upgraded. Generally, it's good practice to keep ArcGIS Pro and Enterprise at the same level but depends on your users workflow. Are they mostly stand-alone users, do they publish web services, do they use an enterprise geodatabase, etc.
One thing I do is block the "check for updates" when I install users desktop software. That way users aren't trying to update beyond the current version of Enterprise installed.
