It’s unlikely that you’ll turn the prop by hand enough to prime the oil pump, and thereafter supply any meaningful amount of oil to the bearings under pressure. It’s more about breaking the sticktion of very cold oil, particularly single weight, on the high friction surfaces like the cylinder walls. When the engine is freed up a little inside, the starter does less work to start the engine. If the oil is that cold, so is the battery. Some older large continental powered Cessnas had oil dilution systems for this purpose. As you operated the system, some gasoline was injected into the engine oil to reduce its viscosity. Once the engine was running, the gasoline would burn off. I’ve only used one of these once, in my early days, and have not seen one at all in decades. Probably multigrade oils made these systems seem unnecessary, and preheating became a lot easier. Many pilots I know will carry a very small generator to run the preheat, when they know that they’re landing away from electricty.
That said, I still do not advocate this, unless you know the airplane very well, and there is no possibility of an effective preheat. If you know that plane that well, you should have made a plan for preheat. When I was the second pilot of the Aztec in far northern Ontario in the winter, I was assigned to take a cab out to the airport during a layover, unwrap the engines, and run them to keep them warm. Every three hours at the longest, while we waited for our passengers. After a few years of this, they bought the PT-6 powered Cheyenne, then it did not matter any more!
A brand new vacuum pump should be fine turning backwards, but as the vanes wear, they are more sloppy in the grooves of the hub, and can cock over sideways and break, even breaking the hub too. I have seen this. Usually when that happens, the vacuum pump jams, and the drive shears too, but you were already replacing it anyway. My first vacuum pump on my 150 lasted more than 3500 hours in service (as did the engine), as the previous owner, and I were both careful with it.