Rye will grow, especially in the fall as the leaves drop. Rye cannot handle much foot traffic though - but will be OK the first fall. In my area (central NY) there is a wild grass that will grow in shaded areas. It grows natural if we keep the trails mowed once a year. It has a very narrow blade, and is kind of wispy - but it grows thick, and stands up well to foot traffic, and light vehicle traffic. The deer will not eat it though - we were able to mix in some white dutch clover in the sunnier places, the deer use the roadways to travel on.

If you can....the best way to benefit the deer with your raodways - is to cut back brush - 10 -20 ft on either side of the roadway - and fertilize it. Cut it back every 2-5 years - the browse will be thick, and more sunlight will reach the roadways - for whatever mix you end up with.