In an enterprise with JIRA already in production and being used every day, deploying Structure plugin and making it available to everyone might be disruptive – in a good sense, since Structure adds a whole layer of useful functionality to JIRA, but perhaps also in a bad sense, if the users are accustomed to their stable user interface and don't appreciate changes that they do not expect.
As a JIRA admin, you can deal with that situation quite easily by deploying Structure gradually.
Structure can be limited to a number of users – see Restricting User Access to Structure. The users who do not have access to Structure don't see Structure's footprint in JIRA in any way (with one exception, see below).
A common path to gradual deployment is:
In the same way, you can gradually enable Structure project-by-project. See Who Has Access to the Structure for details.
Some Structure features can be turned off – see Turning Off Optional Features.
One notable feature is Activity Streams. For technical reasons, even if a user does not have access to Structure, they will still see "Structure" as a possible Activity Streams Provider (although they won't see any events coming out of it). You can turn it off.
Another optional feature to consider is synchronizers. Synchronizers are powerful tools, but they may be harmful if applied carelessly. You can turn off synchronizer modules, or check who in your JIRA has Bulk Edit permission.