The sun would be needed if you wished to produce seeds on that Hairy Vetch but it may well grow fairly well otherwise in low sun areas. Full sun areas get 4 to 6 hours of sun or more. Semi shady areas get 2 to 4 hours of sun, while shady areas can be divided into heavy or light shade because some areas get bright light if no direct sun.

I'm not sure if this will help you, but Peaceful Valley has a good cover crop chart. I used it to find a cover crop that would work in my backyard. Unfortunately, it looks like the link is broken ( Cover Crop Chart, but I have the hard copy here. According to their chart, shade tolerant crops include crimson clover, mini-mix grass clover, strawberry clover, and sheep fescue(covar).

Don't F'n do it!

I put it in my gardon to be 'organic'. What did it do? Immediately spread to my 20 acres, and my neighbors. I've already put down 200 gallons of herbicide to keep it from taking over. Thanks, Elliot coleman, you prick.

To temper the invasive statement, that quality depends greatly on conditions, climate, soil etc.
If you let it drop pods, then it's reasonable to expect proliferation. It also spreads by stolon.

You could try buckwheat; though not a legume thus not N fixing, will grow on almost any soil. If you let it drop seed it will be back, but it's very easy to control and provides lots of green material.

Jeff needless to say
You're just not wild about Hairy
although Hairy is wild over you

any Judy fans?

Major laugh at your expense, Jeff, and I do know it's not even funny. For any of the cover crops that can become invasive,cut 'em just as they are coming into bloom. I use purple vetch successfully this way.