No. When you have sticky shutter, you want to use lighter fluid, xylene, or other suitable solvent to dissolve the grease. High speed, small friction surface should not be lubricated with any fluid. They are usually surface treated to minimize friction anyway.
I am not an Alphax shutter expert (though I've worked with one in the past), but in Copal and Seiko lens shutters, there are only a couple of places that need to be lubricated, and each one of those places require light machine oil held at the tip of a pin, or less. One place requires watch grease (lithium or molybdenum grease) but again, an amount is very small. Any excess of grease or oil will result in similar sticky shutter failure soon.