I have a couple bags of grass shavings leftover from mowing the lawn and was wondering if I work the grass into the soil would that accomplish anything meaningful?
Soil: Do Not Disturb!
Yes, chemical free grass clippings left on top of the soil are a great mulch for your garden. Don't till or dig. Let the natural micro organisms found in soil do their job. In healthy soil, earthworms help decompose the grass clippings. When you use a tiller or dig, you destroy the macro pores and the strands of arbuscular micorrhizal fungi. Anyway, do not disturb the soil in your garden and discover the benefits of mulch!
First, it sounds like you've had them in a bag for a while and depending on temperatures where you are, they may already be slimy and smelly. Otherwise, it will add to the organic content in the soil, but you can get the same result by applying it as a layer over the top and letting it rot down if the clippings are fresh. Doesn't look very attractive after a week or so, and shouldn't be applied more than about an inch deep, but it saves digging in. Safer to dig it in on unplanted ground - benefits to actively growing plants vary - can be beneficial or deleterious, depending on what you're growing and whether its during the growing season or not. Certainly, working grass clippings into an empty vegetable bed a few weeks before planting can be useful, but not massively. One caveat though - if you have used chemicals on your lawn and these are the clippings from it, best composted and not added to the ground.
Alternatively, layer the clippings into your compost heap.