I've heard of that too. But it's supposed to work better if it's raw honey, unpasteurized. I can't find any at this time of year, so I've been using the pasteurized honey as a mask with a few crushed aspirin tablets. It does seem to speed healing, but the aspirin will make you peel a little.
I've read that raw honey is an antiseptic and moisturizer. So it can't hurt to try. But keep in mind the honey will drip down your face. Plus I think nothing feels more luxurious than slathering honey all over your face! 
I found the mask here
I usually use a little more honey and wet the aspirin with a few drops of witch hazel.
I used this last night on a newly forming pimple (not quite a cyst, but had the potential to be big). I put honey (I *think* it's raw, but I can't be sure as it's local and the label is very minimalist) on the spot and covered with a small bandaid. This morning, I pulled off the bandaid, and noticed an oil spot in the middle of the band-aid's gauze area. I'm sure this was the honey/bandaid soaking up the stuff in the cyst! The cyst is still there, but it is no longer painful and appears less inflamed. I work from home so I'm continuing to treat it with honey today. Fingers crossed it disappears.
FWIW, I've heard that honey does two things to acne - either shrinks it into nothing, or quickly brings it to a head so it can be extracted without much ado. In my opinion, these are both very favorable options. Fingers crossed it keeps working!