Absolutely - rabbits love fresh stuff, and alfalfa is no different than any other veggie to them. It is pretty potent stuff, so a small handful is plenty each day to get some greens in.
Rabbits also love cabbage, broccoli, kale, clover, and parsley. Broccoli and clover make good sprouts. We avoid bean sprouts for most animals (except pigs), some do not do well on raw beans. Beans are best for them cooked or fermented (bean sprouts do ferment well).
I find it is generally more efficient to give the rabbits broccoli and cabbage than sprouts. They eat so much sprouts, whereas 3 leaves of cabbage tossed in to mama and babies is much simpler, and not horridly costly even if I have to buy organic. Next year I'll grow my own and make sure to have cabbage, kale, and broccoli growing into the winter months, and enough cabbage stored to make it through when I don't have crops ready. This year we had a crop of immature cabbage and broccoli that was not going to have time to mature, so we fed a lot of it to the rabbits, leaf by leaf. Our breeding doe would absolutely SNATCH that from our hands. I ate a lot of the immature cabbage also, and it was SO GOOD - much more flavorful and tangy than the white cabbage heads.
I am still feeding our rabbits mostly pellets and hay, but after we get onto property, I'll start working on completely natural feed for them. We'll do this with our dog also, when we are in a position to do so. We should have enough meat scraps from butchering, along with grain and veg products, to come up with a good balance for a dog. Our goal is to not have to buy any animal feed at all, and to raise animals that are healthier and more disease resistant than medicated animals. So far things are looking good.
We ran out of veggies and sprouts for the chickens and goats for a few days, and their production declined. We restocked a couple of days ago, and as of yesterday, it is coming back up, so fresh stuff really does make a difference. Right now, I need the eggs and milk so badly to keep coming up out of severe nutritional deficiency, that every cup of milk and every egg we get makes a difference, so I notice their production.
Our chickens are under lights, from 7:00 am till 9:30 pm, and we are getting between 5 and 7 eggs per day out of 8 hens, even when it is storming, below zero, and howling winds drafting through the garage where they are kept. They are bantam cross hens - a mixture of Cochin, Dutch, and maybe some d'uccle or d'Anvers thrown in. They are a hardy bunch though, and sturdy layers.
The cool thing is, you don't actually have to give them a LOT of sprouts or veggies. A couple of handfuls of sprouts is enough for a brooder full of chicks, or 3-4 hens. A single leaf of cabbage for a rabbit, or a single leaf of chard for a goat, is enough to make a difference. Half a cup of sprouted grain will do the same.
When it becomes a lot, is when you have a lot of animals. We have enough now that keeping up with the demand when we did not have a chance to plan ahead from a summer garden, is pretty hard. I have to plant something every day now to keep up with it, and constantly maintain the fermented mashes. But this is the way of life we have chosen, and it is only going to get more demanding as we add more animals, and as those animals multiply, so I have to keep streamlining to make it work efficiently and economically.
For chickens, the rule is: Greens, Grains, and Grubs. Free ranging, they'd get insects for protein. In containment, we have to provide an alternative - we do that by cooking and grinding meat scrap (this year we got a gamey antelope that we could not stomach, and we've been cooking and grinding that for the chicks and chickens). You can also do it by using sunflower seed (chicks need them shelled and broken), thistle seed, or cooked or fermented beans. We usually use a combination of those, plus a little bit of meat.
This spring, we'll be investing in a Soldier Fly Larvae system - the commercial size. That way we'll have self-harvesting grubs for the chickens and ducks to feast on each day. We have redworms also, but I will NOT cut those up for the chicks. There are some things I just won't do, and chopping worms would be a messy job because of all of the vomit we'd have to clean up!
We will be traveling this weekend to Texas to meet with some people about a place to stay temporarily. Not what we planned, but a great blessing.