It will but in small amounts. Depends on how good of a flush you do. Given that it's that bad, it should really be driven for a week or two with water and flushing cleaner, as long as there's no chance of freezing. You say cold, but my definition of cold is the weather outside my house right now, 20°F. (just looked at weather for texas, low is 31 for tonight but after they're plenty safe) After a week or two of water and flushing fluid, I bet a ton of that sludge will have broken up and surfaced in the rad, which you must flush the system again and maybe use the same stuff until it stays clean.
