Is it possible to determine whether or not this is specified in the
service manual for the particular Cessna aircraft I'm flying? It's
a 172N model. Are the service manuals available online?

Cessna gives NOTHING away. Paper copies of their manuals will
start at around US$180, and if there's any temporary revisions they
charge $12 or $15 for two or three pages.
The 172 manuals I have here (L and M) call for some "bounce."
It's standard aircraft practice to ensure that full travel is obtained
at the engine device, whether it's throttle, mixture, carb heat or
whatever. Even flight controls should hit the stops at the control
surface's mechanism before the cockpit end hits anything. Control
systems flex and stretch, especially under load.
Many companies will publish manuals or other service
information on the 'net to make sure it's available, and others want
every buck they can squeeze from it. Cessna requires a rather expensive
subscription ($360/yr) for service info (updates, service bulletins and
service letters, etc.) while American Champion maintains a website to
do the same thing. Lycoming's website publishes a service manual
currency page, but McCauley and Cessna do it only through subscription.
All of them are owned by Textron, yet there's no consistency.

Dan