DWR won't really make your shoes waterproof, but it will probably help a bit. DWR makes the fabric absorb little/no water which will cause rain to bead up for awhile, but it will eventually wet out. Stepping into a puddle will still soak through.
It should decrease drying time, though, since the shoes won't hold as much water in total. Sorta like in the early 80's when we'd spray our blue jeans so the snow wouldn't stick and soak through (yeah, cotton and maybe acid-washed. Mistakes were made).
I had a similar experience a few years ago where my shoes got soaked before a cold night. I really didn't enjoy putting those semi-frozen shoes back on in the morning. I reacted to that by grabbing some of the Neoshell Lone Peaks (on closeout somewhere...). They do get warmer than other shoes, but I also have very
dry feet so I don't have issues with blisters or sweating.
Super-dry feet are my super power. Great for hiking; not so great for fighting crime.