The Hawthorne Effect, if present, is desirable in an agile framework.
Reasonable Question; False Premise
I think the original question stems from a false premise. The premise seems to be that changes to observed behavior as a result of being observed are intrinsically less valuable than unprompted or spontaneous changes.
Continuous Improvement Through Introspection
Agile practices are built around tight feedback loops and continuous inspection of the team's process. The whole premise of agile is that improvement is driven by observing the outcome of a process and making continual adjustments to fine-tune the results.
The Scrum Alliance defines the framework as follows:
Scrum is a simple "inspect and adapt" framework that has three roles, three ceremonies, and three artifacts designed to deliver working software in Sprints, usually 30-day iterations.
When you drive, you don't put your hands at ten-and-two, hold the wheel with an immovable death grip, and hope for the best. You make constant course corrections--generally minor, unless you're careening out of control or making a U-turn, but constant all the same. One might even say that one metric of good driving is the ability to make continual adjustments so that large corrections are not necessary--such as to avoid the fast-moving sequoia that just jumped in front of your car.
Scrum bakes a lot of this into the various required meetings, but the Sprint Retrospective is the epitome of inspect-and-adapt. Since process is made up of people, process change is often dependent on behavioral change to succeed.
Because Scrum is about continuously inspecting the process, and continually adapting the process to current circumstances, there are two obvious conclusions one can draw.
Behavior will be constantly observed. Unobserved behavior is an indicator of a hidden process, and needs to be made visible.
Behavior change does not need to be permanent, or retroactively measured to any great extent. What matters is whether the current process is supporting the team's current objectives.
Whether the reason is the Hawthorne Effect or some other social driver, the constant adaptation to observation is a clearly-stated goal of agile frameworks such as Scrum.