Much is made of this fact -- advice that we should plant clover in our lawn to give the grass a boost...
Have a read of the following "lawn care" article as it dispels that misconception:
If you believe the information given in the article, which I do -- Clover taking over a lawn is a sure sign that the soil is nitrogen deficient and the clover isn't going to help the grass. Period.
Please bear in mind, the article doesn't directly answer your question, but I believe it does give some relevant information pertaining to your question to make it a worthwhile read.
Have a listen of Gardeners' Question Time podcast, Colne and starting listening at 33mins:38secs in.
Chris Beardshaw debunks a longstanding myth about nitrogen-fixing pea shoots.
Below is my poor effort at transcribing what is said:
Peter Gibbs: How many of you leave your pea & beans roots in the ground to get the benefit of the nitrogen that they've fixed through the Winter?
Peter Gibbs: A few hands going up there, so do I, but Chris is going to tell us we're doing it all wrong
Chris Beardshaw: Well, not necessarily doing it wrong, the principal is true and it has in fact been going on for ages hasn't it?
My grandfather taught me that all the legumes, the pea and bean family are nitrogen fixing plants.
That's to say they absorb nitrogen or in fact there is a bacteria that absorbs nitrogen on their behalf and in return the bacteria plugs into the root and gets simple sugars out of the plant, so it's a kind of symbiotic relationship.
The plant gets the nitrogen and that's why we've left our peas and beans roots in the garden thinking we're going to improve the nitrogen status of our soils.
That is until some research was recently carried out which has proved that the nodules that are formed, are present in very high quantities and that about 40% of the plants total nitrogen reserve is at the root in those nodules prior to flowering.
However as soon as the plant flowers the majority of that nitrogen then moves not into the stems and leaves, it moves away from the root into the flower, and into the pods, and of course the seeds, the peas, the beans themselves.
So much so that after harvest the nodules and the roots contain less than 3% of the original nitrogen, so if you're leaving your pea and bean roots in after harvest, actually there's very little point other than just improving the general soil structure.
Peter Gibbs: So we're not wrong, just misguided?
Chris Beardshaw: Yeah, one of the things if you're using green manures, very often we use peas and beans or things like winters beans as a green manure. But if you think about how we use them, we dig them in before they flower, that's where you get the benefit of all that fixed nitrogen. Plus all of the nitrogen which is in the plant, the upper part of the plant.
Don't bother leaving them in ground expecting to get a high nitrogen flush after they've fruited.
I'm currently in conversation with Chris Beardshaw, Peter Gibbs and Gardeners' Question Time, trying to get further information about the aforementioned study (hopefully a link to the actual document). If I'm successful, I will update this answer...
So far I've got back:
Peter Gibbs: Chris quoted a study which found legumes only fix nitrogen up to the flowering stage, so leaving roots over winter is pointless.
Chris Beardshaw: The important element was the huge reduction of available N in the nodules after onset of flowering, against popular beliefs.