No. I have seen folks on the CABE recommend doing this, and I question if they have actually done it themselves. It works, but with very poor results. The acid bath must be consistent and that is hard to do with a wet rag. It will take any rust stains out of your paint. Items must be completely submerged in the solution, otherwise you will end up with a definite" line" between the treated area and untreated.
I have used OX many times and have tried partial dips and the rag method. Possibly you could clean the area around the treated spot after the the rag soak, with a cleaner type wax to blend in the untreated paint. A wet rag is no substitute for a submersion in the solution.
I just took a shower and was thinking over your question, so I will edit this post. First of all what color is your bike? If it's blue that's good. If it's red forget about the OX, if your bike is a nice one. I soaked two pre-war red, original paint Colsons on the same day. Both red and rusty, identical looking frames. The first one I soaked for about 4 hours. It turned out great. No damage to the red paint. The second one I took out of the bath after about 20 minutes. as the paint started looking pink.
It turned out all right....sort of..... but still, after only 20 minutes the paint was visibly lighter. Go figure??
Shawn Freqman's pool is the route.