Yeah, still not great. Even with a bunch of soap you're still going to have some grease that doesn't get emulsified with the soap and water.
The way soap works is by attaching molecules of oil to water, but it requires a lot of agitation/energy for a complete emulsion that won't quickly break down to its constituent parts again.
If you're in a situation where you have to pour grease down your pipe, continue your soap method, but let the hot water run for a min or two before, during, and after you pour the grease. The hotter the better.
Less likely to cause issues, but it might still leave residue on your pipes over time. That said, I also do that. Wipe up what I can with a paper towel, then dilute the rest with hot water and soap