You can. Alfalfa pellets and cubes are typically make from over mature rain damaged hay that can't command a premium price in the horse market. There is more leaf shatter from extended drying losing leaf matter (the more desirable and nutritious portion). If you ferment your feed it is simple to add a handful to the bucket to add some green. My preference is to use regular alfalfa hay. First off I have an abundance of it for the horses but it's going to be a superior product with more leaf, when there is a shortage of free ranging it will provide hours of scratching and entertainment and cheaper. The leftover stems just become bedding.
I haven't seen alfalfa meal at the feed store in decades. It's typically a feed milling ingredient. Normally listed as "forage product" on the feed tag. It will have a high portion of stems, a portion they would normally not eat. As far as protein content, it is all over the place. Could be as low as 12% or as high as 18%+. In buying a bale of hay look for small stems, green, loaded with leaves, sweet smelling (no fermented tang) no flowers (purple or white).