No, the pedal is not limited to depressed or at rest position. The use of pedal is quite complex and a science.
Half pedal is not a recent development. That statement from the above poster is incorrect. The use of half, flutter and other pedaling increments has been in play ever since the piano was invented. Chopin was known to flutter pedal a lot and there are stories that his students would lie on the floor and watch his foot move so they could understand pedaling. Chopin however never notated clear pedal directions and his markings are often argued over. Beethoven intended the use of flutter and half pedal in may of his sonatas. One example is in Sonata Op. 110, the middle section with the repeated "c's" has a long pedal mark written underneath it, but in one of his letters he says that the pedal is to be rapidly moved and not to be fully depressed. Liszt was a big proponent as well. He often used it to create a variety of tonal colors and one use is in the Db Consolation. The low bass notes are written as whole notes but it is impossible to holed that note as the L.H. has to go and play accompaniment in the tenor while the R.h. has the melody. If one holds the pedal down the entire time, everything gets blurred, but like Beethoven, Liszt told his students to half pedal so that the Db i still sounded but the harmonies would become blurry.
Legato is never achieved by pedal. Legato can only be achieved by using the fingers and the ear. The pedal joins the notes but does not make the notes legato. Legato is the connection from one note to the next. The connection is not only tonal but also is affected by dynamics. You can play 5 notes with the pedal down at 5 different dynamics and different tonal touches and that does not mean legato. Legato is a continuous line that can only be achieved using fingers. It is best to practice without pedal so one can develop excellent legato.
Now, onto pedaling. The use of half pedal and flutter pedal is very effective in creating a variety of tonal colors. The pedal remember is a coloring device, it is not a sustaining device. People learn it as a sustain device and most teachers do not teach that it is used to give shades and colors to your tonal palette. Just like an artist has a variety of shades of reds, blues and yellows, a pianist can use the pedal to create these tones.
Now this only works on an acoustic piano, not a digital keyboard because the digital instrument even if it is slightly depressed tells the computer to "sustain notes". Half and flutter pedal can only be done on a real instrument. By lifting up the dampers a touch part of the string vibrates, or possibly 2 out of the 3 strings in the upper register and 1 out of 2 strings vibrate and sustains in the middle.
This type of pedaling is very effective for all music! I tend to flutter pedal a lot in scale and running passages. I would never hold the pedal down because the sound would blur, but using half pedal catches some tones and allows for a touch of harmonic color while maintaining clarity in the passage work.
With flutter pedal I move the pedal up and down very quickly... However, every piano is different so you have to listen carefully to your pedaling. Sometimes what I rehearse works well on my piano but not on stage, so things have to be adjusted instantly for success. And this is done by listening! It takes intense hearing to listen to all that is happening while we play.
You can 1/4 pedal, 3/4 pedal... but everything is adjusted with the ear.
I use a lot of half, flutter and other types of pedaling in Debussy because of the different ranges of colors and contrasts required! But I use all these techniques in all pieces I perform. And specifically in chamber music. a pianist has to be very careful that their pedaling does not interfere with what the other musicians are doing.
Pedaling is not just lifting up and down, its the use of a very sensitive device that enhances one's performance if one has a sensitive ear and knows what they want to come out. The pedal is not used for legato. It's purpose is not to join notes.