I've done it. You just don't want to age it in there, oxygen permeates through the plastic over time, and oxidizes the mead. But you can damn sure ferment it for a couple of months before you bottle it in glass.
For a basic recipe, just go with 2.5 pounds of honey topped up with spring water (for the minerals) to the shoulder of the jug. Shake the crap out of it to get some oxygen in it and make sure it's all mixed up. Use a cheap wine yeast, with nutrients. Keep it in the 60's for the first two weeks.
Or get one of those 3-packs of Fleishmann's from the grocery store. Put two of the packs in boiling water to kill it, then pour into the mead. Then follow the directions to rehydrate the 3rd pack, and use that to ferment. The yeast from pack 3 will use the two dead packs as nutrient, along with the minerals in the spring water, to ferment the honey.
It's that simple.
If you want to go adding more honey and other ingredients, it gets more complicated. It can be as simple or as complicated as you want to make it.