Is it possible to use an accelerometer as a route finder?
Yes, this kind of system is called an Inertial Navigation System.

https://www.rs-online.com/designspark/what-is-inertial-navigation-for-adasadvanced-driver-assistance-systems-murata-accelerometers


  The measurement that an INS generates is relative to their last known position, so even after an inertial navigation system has been turned on for several minutes, it cannot specify where it is, but it can ascertain that it hasn’t moved. If the INS knows where it started, it can easily work out where it is, based on its own measurements. That is how spaceships and aircraft successfully navigate using an INS – because they know where they started from.


These systems have been used on aircraft for decades as they do not rely on GPS. They are self contained &amp; reliable methods to navigate, especially through challenging weather systems.

AFAIK there is no Arduino library to create an INS, but it is trivial to create a basic tracker for "distance moved" in X, Y and Z axis. 

Hint: area under the curve