This video seems to suggest to me you can. What is the technique called and how is it played?
Yes. There's a lesson on how to do it on YouTube. For the right hand, place the back of finger 2 on the centre of the string. Pluck with the thumb (finger 1), and immediately remove the whole hand to allow the string to vibrate. For the left hand, the technique is a bit different - the palm of the hand blocks the string instead.
You end up with a note one octave up from normal, but with a distinctive sound.
If you're not sure where the centre of the string is, here's a trick I found. Keep plucking the string with a finger of one hand, while gently sliding finger 2 on the other hand up and down the string. Most of the time you get a dull thud, but at the exact centre, the string will start to ring.
Harmonics can be played on any stringed instrument. It involves touchng the string at a node. The simplest is the octave, which is exactly half way along the string. This gives a sound an octave above the open string, as it divides the string into two vibrating parts, which vibrate twice as fast as the original. Easy to do on guitar, as is the one third touch, making a sound one fifth above the original. Obviously, there are two nodes for this. If you want to do this on guitar, they're above the 7th and 19th fretwires.
Yes, harmonics are beautiful on the harp, and quite common.
The symbol in sheet music for a harmonic is a small circle placed above or below the note head, usually opposite the stem. There has been some variation in how the harmonics are noted, as the legendary Carlos Salzedo liked to write the harmonic in the octave where it will sounds rather than where it is played. However, most composers now put the harmonic note where it is played and it will sound one octave higher. If a composer wishes to use Salzedo's method it is customary to inscribe "Harmonics are written where they sound and played an octave lower" in the preface notes for the performer.
Learning to play harmonics well in both hands is a significant topic in harp lessons. The hand position for left hand harmonics is quite different from that of right, and there are stylistic differences for both hands among different teaching methods. Double and even triple harmonics can be played, depending on which notes are desired and which hand is playing them. Playing harmonics on different harps will require adjustment because there is so much variation in the physical dimensions of different brands and styles of harp.