The global mean sea level (GMSL) we estimate is an average over the oceans (limited by the satellite inclination to ± 66 degrees latitude), and it cannot be used to predict relative sea level changes along the coasts. As an average, it indicates the general state of the sea level across the oceans and not any specific location. Local tide gauges measure the sea level at a single location relative to the local land surface, a measurement referred to as "relative sea level" (RSL). Because the land surfaces are dynamic, with some locations rising (e.g., Hudson Bay due to GIA) or sinking (e.g., New Orleans due to subsidence), relative sea level changes are different across world coasts. To understand the relative sea level effects of global oceanic volume changes (as estimated by the GMSL) at a specific location, issues such as GIA, tectonic uplift, and self attraction and loading (SAL, e.g., Tamisiea et al., 2010), must also be considered.
We do compare the altimeter sea level measurements against a network tide gauges to discover and monitor drift in the satellite (and sometimes tide gauge) measurements. This is discussed further in the tide gauge discussion.
GMSL is a good indicator of changes in the volume of water in the oceans due to mass influx (e.g., land ice melt) and density changes (e.g., thermal expansion), and is therefore of interest in detecting climate change.