Yes, it can but it’s very unlikely and would indicate a poor design on the power regulation of the GPS.
A bad contact can generate heat and arcing but it’s not relevant to a car’s lighter socket.
What is more likely is a bad connection with possibly oxydation coming into play; that would act as a resistance and provide a lower voltage for the GPS’ power regulator.
This forces the regulator to draw more current to compensate and will generate more heat until the regulator fails.
Now this would take a bad design since most regulators are protected against this, but in this era of cheap Chinese designs where safety features are ommitted to save money, it wouldn’t be the first device where regulation is not down properly.
Regulation at the car level could also be a problem: if a device gets frequently connected / didconnected (we’re talking on a micro scale here, with road vibrations for example) the regulator may over / under shoot when trying to keep its output stable.
So, in essence, it is possible that this caused the problem but it wouldn’t be the most likely cause.