As far as I'm aware, the Garmin 'calibration' only works at a point of known elevation. So, on my Edges 800 and 1000, I am able to specify the 'home' location and elevation for instance, and when the unit is turned on and recognises it's at that point, it will start its elevation trace at the known value, then use the barometer to track changes. If it doesn't know any other values for other locations (and I'm not sure it can), the trace will be distorted over time by changes in atmospheric pressure. This is one of the reasons why barometer-equipped GPS unit cumulative elevation calculations aren't that accurate, and why Strava and Connect and other online data-gatherers offer the option to correct the cumulative elevation total by using whatever elevation grid data they have available. Of course, that grid may be quite coarse and thus be even less accurate.
GPS elevation is another subject, and in cycling units is very inaccurate, which is why the grid correction above is automatically applied to non-barometric GPS tracks recorded in Strava and Garmin Connect.