This might work, but probably not as well as using dish soap and water.
Because greases are made up of nonpolar chemicals, they are best dissolved by either nonpolar solvents or detergents. Nonpolar solvents are fluids made up of nonpolar molecules, which stick directly to the grease molecules they dissolve. This category includes things like acetone, petrol, and mineral spirits. These make good degreasers, especially if they're volatile enough that they will evaporate (otherwise you've just replaced one oily substance with another). WD-40 is in this category.
Polar solvents similarly stick to polar molecules or ions, so that's why you can use water to wash something covered in salt (where it dissociates into Na+ and Cl- ions in solution) but trying to do the same with acetone would be much less effective. This category includes water and alcohols.
Detergents (such as dishwashing liquid or laundry soap) contain chemicals with large molecules having a polar end and a nonpolar end: the polar end sticks to (polar) water molecules and the nonpolar end sticks to the grease molecules, allowing both detergent and grease to be washed away by water. This might be your best bet for common household chemicals, google shows quite a few people reporting good results for using it to clean bike chains.
EDIT: After prompting from gschenk I'm reminded that ethanol is actually a decent solvent for nonpolar molecules as well, due to basically having a polar end and a nonpolar end. Still, as a spray it will just slightly dilute grease. You might be able to use it by putting the chain in a container with it and shaking it around a lot, but you would have to do the same with a detergent, and the other additives in the sanitiser aren't going to do you any favours.