This is an interesting idea. I've just planted out my strawberries....
I'm assuming hairy vetch is
vicia villosa I don't have that, but I do have Vicia cracca (tufted vetch) which apparently is very similar. It does seem quite vigorous, but the OP seemed to think the strawberries don't mind. I guess some Nitrogen fixing and mulch wouldn't hurt. Has anyone else experimented with this combination, or have other suggestions?