I agree with what Pamnock said. And that's coming from a pretty good source if Pamnock is an ARBA judge. I have an article that Doc Reed wrote on this subject years ago. The increased protein should help cause the rabbit to molt quicker, but giving protein beyond a certain point doesn't really make the rabbit molt any quicker. The rabbit will use what protein it can absorb. The excess protein gets excreted out of the rabbit's system in the urine. This causes the rabbit to have to pee more and the Nitrogen from the protein can cause there to be more urea. So yes, as Pamnock said your rabbit will probably have to drink more water. So once you get to the point where the rabbit is peeing excess protein out, it doesn't do any good to give a higher percentage of protein. And on older rabbits that can be hard on them.
Also, while protein itself won't make a rabbit fat, it is a high energy ingredient in your rabbit's diet. When your rabbits eat carbohydrates the excess energy from carbohydrates normally gets stored as fat. So if your rabbit is getting all of the energy it needs already from the protein, the carbohydrates it eats may get stored as fat, tending to make your rabbit fat because that energy from the carbohydrates is excess energy. This also factors into the fat or lipid ingredients because unused fat energy gets stores as fat. In my animal nutrition classes they would say "fat goes to fat."
As far as feeding Alfalfa hay, that really may not increase the protein level of your rabbit's diet. In the book "Rabbit Feeding and Nutrition", the author states that alfalfa hay contains 15.3% crude protein. If you do a web search on crude protein in alfalfa hay you'll find that many studies have been done. The studies tend to state that the crude protein level will vary depending upon the time of bloom when the hay is harvested, the cutting, and even how many years that hay has been planted. The results seem to vary. I think the variance mainly has to do with what percentage of leaves to stems the hay has. The protein is mainly contained within the leaves of the plant. The stem is mainly fiber and has little protein. Leaves will tend to fall off the hay and not get bailed if the hay is let to sit too long in the field. You will also notice that red clover hay tends to have higher crude protein levels than alfalfa hay. "Rabbit Feeding and Nutrition" states that it 17.3% crude protein. That is 2% more than alfalfa hay. Red clover hay also tends to have bigger leaves than alfalfa hay and may be comprised of more leaf portion compared to alfalfa.
Most rabbit feeds average about 16% crude protein. So if you are trying to up the protein by feeding alfalfa hay, you are actually probably decreasing the protein level. With red clover hay you may be increasing it.
Doc Reed mentions feeding rabbits "milk pellets" to temporarily increase the protein level. And to also increase the oils the rabbit gets to help improve the fur. Some oils that rabbit breeders tend to use are wheat germ oil, peanut oil, and sunflower oil. Wheat germ oil is also a good source of Vitamin E which helps with fertility. Milk pellets are given to other animals typically to help increase milk production and therefore are high in protein. Adding a teaspoon or so to the pellets could help increase the protein your rabbit gets. Some rabbit breeders will alsoadd Calf Manna which is also high in protein to help add a little extra protein to the diet.
When you increase the protein your rabbit will be molting faster. Rabbit hair is made of protein. When you give your rabbit more protein it tends to produce new hairs faster, pushing the old hairs out. Those loose old hairs need to be brushed out. For about a minute or so every day the rabbit should be brushed out by hand. Lightly wet your hands with water then rub the hands from front to back. The loose hair will stick to your hands. Just rub your hands together to remove the hair on your hands. Unless you have a wool breed rabbit don't use a brush. Brushes will damage the hair follicles and pull out non-loose hairs which you don't want to do.
If you are doing something like this for a show, timing of when you start is key. Because you want your rabbit to molt out all of that old fur by the time the show comes around. Then once your rabbit has that new bright shiny coat of fur, you still keep feeding the oils according to Doc Reed, but you reduce the protein.You can do that by pulling away the milk pellets and even feeding a little timothy hay which is lower in crude protein at about 9% crude protein or so.
Also be careful of the show enhancers. There are two main Enhancers out there that you can add to the feeds. The one created by Doc Reed is "Doc's Rabbit Enhancer". The other main one is called "Showbloom". These two rabbit ration additives are completely at opposite extremes. The website below lists both of them:
https://bunnyrabbit.com/price/supplements.htm
When you click for more info on both, take a look at the minimum crude protein level on both. Doc's has 14%. That is low. Show bloom has 30%. That is very high. Show bloom is more made for blowing that coat real quick and getting in a new coat of fur due to its high protein level. Doc's is just the opposite. Once your rabbit gets that good coat of fur you feed his and it will help keep that coat of fur in place. If you kept feeding Showbloom after your rabbit got that great coat of fur it would likely blow that great coat in no time because that high protein would create new hairs, pushing out the coat of fur you want to keep.
So its good to learn what the different ingredients and types of nutrition do.
