I'd use it especially if it doesn't have added salt.

Alfalfa Hay can be a good mulch material and can add many nutrients to your soil, however much of that hay has been sprayed with several synthetic products to suppress weed growth, and maybe to aid in control of some insect pests. While Alfalfa pellets, hay that has been processed into animal feed, may have sodium added to enhance flavor as well as to partially supply the sodium needed by the animals being fed, even packaged hay such as this usually does not have any sodium added under the assumption that the animals this is meant for have access to salt blocks.
You can use this in your garden if you are not an organic fanatic.

Alfalfa & molasses are good compost activators. In the fall I've used spoiled alfalfa hay from a friend that really got a pile of horse manure + pelleted bedding cooking.

Might be best to compost first before using in the garden or use spread very thinly as mulch around your heavy feeders. Don't put in planting holes.

I've used plain alfalfa pellets around perennials and shrubs and also put a small handful in a watering can for a few days then used it to water.