I use just about any shred-able biomass as mulch. Grass. Weeds. Leaves. And I include twigs. The only requirements are that they be small enough in size so as not to interfere with a rototiller, and that they not be a plant variety that will root themselves in my garden. Some of the bushes around here sends out roots fairly readily.
I break or cut twigs into lengths not more than 6 inches. Then I scatter them lightly in the garden aisleways.
...lay mulch in aisles
...move aisle mulch onto growing veggies as they need more mulch, then replace the aisle mulch with new
...after harvesting veggies, rototill in the old mulch that had been around them.
...plant new crop and when it's ready for mulch, pull the mulch from the aisle onto the veggie bed.
The reason why I cycle like this is twofold. First, the mulch in the aisles is constantly being walked on. Thus it gets bruised and crushed, resulting in it decomposing easier and faster. Second, I sometimes don't have mulch ready the day that the veggies need it. So grabbing the aisleway mulch is handy and timely.
So what about those twigs? What benefits? Of course they eventually decompose, becoming soil, becoming nutrition for the garden. But I also notice that they have a bearing on soil moisture retention. Twig treated soil holds moisture better. Plus the soil also doesn't compact as badly nor become "pasty". I don't think that the twigs made the soil significantly better right away. But over the years I can see a real difference between the areas that routinely get twigs and the areas that never have had them added.
I don't use lots of twigs, not like covering the ground in wood chips. I just use the twigs that I have. And as I said, they get trod on for weeks then get tilled in. I notice that they decompose slower than the grass clippings, but that is just fine. I'm told that woody material is good for soil fungus ecology. That's a plus.