We were going to plant alfalfa between all our rows and raised beds. I'm starting to think the chicken mix would be better. Would it help keep the weeds down and also still be okay to walk on?
It all depends on what you consider "weeds"
Some would call the clover, etc. that are included in the seed/forage mixes "weeds" themselves.
Since owning chickens, I've come to realize that nearly every green plant that springs up in my lawn has some value. The dandelions that drive my neighbors crazy (they all have meticulously manicured lawns, brimming in pesticides and herbicides), for instance, I see as valuable chicken chow!
I personally, don't mind if my backyard lawn (where my chickens are tractored) is completely "weed-free" and 98.9% Scott's Kentucky Bluegrass, as long as it's green when mowed and supplies my girls with maximum nutrition and enjoyment. I've always had a more informal, cottage gardening style, and have always shied away from chemical pesticide, herbicide and fertilizer use, so this type of turf fits right in with my sensibilities.
If you keep mowing and/or clipping (giving the clippings to your hens), you should be able to keep a nice, green mat that looks attractive enough.
My Pet Chicken also sells a seed mix called "Chicken Salad". I bought a bunch of packets and throughout the winter was able to keep the greens going in a cold frame (it was a very mild winter, so I don't know if it would have worked so well otherwise). It's less of a "turf" mix and more of a broadleaf mixture, with purple top turnips making up a big proportion of it (hens LOVE those leaves!)