Note: I'm not a biologist
The key problem with this is predicting what the human's hunger would be like after the surgery. We can't talk to cows or other ruminents,  so we can't predict what effect multiple stomachs would have on human hunger. On top of that, since this surgery doesn't exist in the real world, I have to wonder if the other 3 stomachs are artificial or transplanted. Is the human even capable of feeling them, or is his appetite entirely based on his natural stomach? Basically, you're going to have to make up the impact on his hunger. Once that's done, you'll want to figure out the potential for fermentation of the food he's eating and what that fermentation will do to the calorie density of the food. It seems that human hunger is mostly governed by the volume of what we eat, rather than the calorie intake. [citation: I have a human stomach] The ruminent process may change the caloric value of his diet, causing him to gain or lose weight. That depends on his diet and his hunger, and even if I had complete details on both, I'm not familiar enough with biology to know how to calculate it, so I'll have to leave the calculations to you.
Another problem with your second question on switching diets is how many calories a human needs vs how many he gets if he replaces his diet with ruminent-digested grass.
None of this takes into question taste. Unless there's some tongue-surgery going on, too, it's going to be tough to make a ruminent diet palatable - whether that's grass or just partially digested food all mixed together.
One more over-all concern: I would argue that any weight loss he experienced would be a sign that he is getting full without getting enough calories, and he will need to force himself to overeat the same way that most dieters force themselves to under-eat. Granted, most of us would prefer that outcome, but given the taste issue and the drastic surgery, this sounds more to me like a human centipede situation than a weight-loss solution.