Can someone actually "fly under the radar"?
In many cases, yes you can fly under the radar because typical civilian radar is line of sight, meaning that it has to have a straight unobstructed path to an object in order to "see" it.

This is because it works by sending a radar signal out and waiting for it to reflect off of something.  If it reflects off of another object, like the ground, a mountain, a building, a thunderstorm, etc. then it won't see what is behind it.

Since the earth is round, flying "under" the radar is flying beneath the coverage area that the radar can "see" directly from where it is, and the height of radar coverage depends on the distance from the site as well as the terrain.

An example is here:



The top half shows how the curvature of the earth affects it and the bottom half shows how other objects can shadow radar (even though is is using aircraft radar, the same principle applies).



That being said, there are other types of radar and other ways of utilizing radar that minimize this problem and make it nearly impossible to fly under it.  

One common type in use is the Tethered Aerostat Radar System:



This is downward looking radar attached to a 25,000 ft. tether.  From 15,000 ft. it can detect aircraft and even vessels all of the way down to the surface of the ocean out to 200 miles.

Another type is Over-The-Horizon Radar which can see further by reflecting radar off of the ionisphere like this: