RE: So what is in the solvent?
Solvent ingredients vary from brand to brand of cleaner. Some use ammonia, others alcohol, some use strong soaps, peroxides are sometimes used, some are real basic such aswater and soap. There are many combinations. It would be near impossible to list the make up of a cleaner since many vary according to brand. That's why I suggested simple water and soap in the tube. That way the barrel is not sitting in a harsh chemical solution that although may keep it from rusting could also damage the metal, bluing, or fiber optic sights (plastic in most cases)of the rifle.
Since rust is the process of theoxidation of metal, I was thinking, as you mentioned,in terms of submersion of the metal barrel in a liquid might impede the oxidation process, thus prolonging the necessity for you to get at the barrel immediately for cleaning. This soaking possibly would also in effect soften any fowling contained in or on the barrel and make cleaning at a later time much easier.
One thing I would do if this was going to occur would be to remove the breech plug prior to submersion in the tank if possible. This would allow the threads of the breech plug area to soak clean also. It sounds like a workable idea. Murphy's Oil Soap is a gentle natural ingredient soap. I would try that and some water as my first test solution. Another one to consider is Simple Green Cleaner. Keep us posted as to the results of your tests. You might be on to something for those that travel great distances from a range to home for example. They could remove the barrel at the range, place it in the tube and solution, drive home many hours later, and have no troubles with removing fowling which had time to set up or cure...
Good luck.