If what you mean are those cardboard milk cartons treated to be moisture proof not only would that be a lot of work but the treatment of the cartons could keep them from getting digested. If you mean the plastic milk containers they would not be a good addition to your soil in any way, although they can make good cloches. I would stick with materials that will eventually get digested, cardboard (untreated) and/or newspaper, builders paper, materials that wehn they do break down will add something worthwhile to the soil and not potentially contaminate your soil.

Many cartons are made of a sandwich of materials. They look like cardboard but have a layer of foil or plastic in between. If you can tear the carton easily it is just cardboard. If it resists it probably has a layer of something in it. Also to stop weeds you would need to overlap the cartons as perennial weeds will very quicky find the light and come up between small sheets of material. Sounds like a huge amount of effort for not much effect.

They may not rot.