It could increase the amount of hay consumption. It depends on what type of tubs you buy and what kind of hay you are feeding.
If you have decent quality hay, I would stick with it and leave out the expense of the tubs. How do your cows look? Are they dumping chunks or cow pies etc?
If my cows are getting decent hay, the only other supplement they get is loose mineral and salt. If the quality of hay is not all that great, I might put out some high protein tubs. The higher the protein the more junk hay consumption in order to put out the fire in their belly.
Jeane (I think it was Jeane) put out a thread on evaluating cow poop a week or so ago. It is good info and on the money as far as i am concerned. I look over the condition of my cows and I look at their poop to determine nutritional needs.