It's actually more of a silicone, something like Dow Corning #33. I've found it to be useful for fan bearings, as it works well as a lubricant on plastic surfaces, plus it won't attack them chemically. As it's a grease rather than a liquid, it won't seep out or stain the label that covers/seals the bearing cavity on the fan, and it also tends to dampen vibration noise simply because it stays in place once applied.
It's a little bit tricky to get it into a sleeve bearing -- probably best to apply a layer to the fan axle after disassembling, dab some on the bearing surface where the axle end protrudes, reattach the "C" ring retainer that holds the axle in the bearing, and reassemble.
It may or may not work, depending on how worn the fan is. I've got an AIW X800XL with stock cooling that I wasn't able to save completely -- it helped, but it still rattles some. So YMMV.
Edit: in looking at your avatar photo, you might also want to add some to the flat circular surface surrounding the fan axle, where it makes contact with that bearing surface in the armature. This would be the advantage to getting the grease in a syringe package, as it makes precise application easier.