Pro gamers in highly competitive, reaction-based games (such as most first-person shooters) usually disable it, yeah.
And I'm not an expert in this either, but I'm pretty sure double buffering is the norm, whether you use V-Sync or not.
One buffer in which your graphics card works on frames (I'll call this "graphics card buffer") and then a buffer into which finished frames are moved, so that your screen can read them out in peace (I'll call this "pre-screen buffer").
There's also "triple buffering", which introduces another one of those graphics card buffers, so that when a finished frame is being transferred from that first graphics card buffer to the pre-screen buffer, then your graphics card doesn't have to wait for that transfer to finish and can instead start working in the second graphics card buffer right away. (And then it transfers frames from those graphics card buffers in alternating fashion.)
So, the delay that V-Sync introduces is not that. What V-Sync does, is that instead of transferring finished frames from the graphics card buffer(s) into the pre-screen buffer as soon as the frame is finished, it waits with the transfer until your screen has finished with reading out the previous frame.
If you don't wait (have V-Sync disabled), your screen will read out some part of the previous frame and then read out the rest from the new frame. On the screen, you'll see this break between previous and new frame as screen tearing.
So, assuming your screen can display 120 frames per second and your graphics card happens to finish 120 frames in a second, then V-Sync will not introduce a delay. It'll wait once with transferring the first frame, but then they'll be in sync and no further delay should occur.
However, if your graphics card is able to calculate 240 frames per second (and your screen still does 120 frames per second), then with V-Sync, the graphics card buffer will be transferred into the pre-screen buffer only 120 times per second, making the graphics card slow down to 120 frames per second as well.
Without V-Sync, the graphics card buffer will be transferred 240 times per second, regardless of how often your screen can read it out from the pre-screen buffer. This means a frame will get loaded into the pre-screen buffer as your screen is reading it out. As a result, you'll get screen tearing and one half of your screen will be from the new frame, with a 1/240 s = 4.167 ms delay, the other half is still from the previous frame with a 2/240 s = 1/120 s = 8.33 ms delay.
So, a few numbers:
120 FPS with 120 Hz screen = 8.33 ms delay.
240 FPS with 240 Hz screen = 4.167 ms delay.
240 FPS with 120 Hz screen = ½8.33 ms + ½4.167 ms = 6.25 ms delay on average.
480 FPS with 120 Hz screen = ¼(1/480) + ¼(1/360) + ¼(1/240) + ¼(1/120) = 4.34 ms delay on average.
960 FPS with 120 Hz screen = 2.83 ms delay on average.
960 FPS with 240 Hz screen = 2.17 ms delay on average.