No,  I would say the size of the material will be reflected in the rate of its breakdown - smaller pieces will break down faster than larger pieces because the smaller pieces have more surface area.  However, it will not change the amount of nitrogen (and carbon) that is needed to cause the breakdown to occur.  I am going to post a couple of links to composting websites, because I think what you are talking about is essentially a composting process - or at least close enough to a composting process that the same principles apply.

There are a couple of factors that need to occur:

you need to have the proper carbon: nitrogen ratio

you need to have proper moisture level

you need to have bacteria present to make the process work.

If the carbon: nitrogen ratio is too high, bacteria will pull nitrogen out of the soil until they get enough to make the breakdown happen.  Not having enough will slow the process down.

If the carbon: nitrogen ratio is too low, bacteria will release excess nitrogen into the atmosphere (essentially wasting it).

Having the straw "lay out on top" makes it prone to drying out, and the bacteria will not work (as well) if the material is too dry.  Having that straw in contact with the soil helps to enable the straw to be at the proper moisture level for the bacteria to work.  If you look at a piece of straw laying on the soil surface, the top side might look dry, but if you turn it over, it will be damp and that is where the bacteria is working to break it down. Having that straw in contact with the soil surface definitely aids in the breakdown process.

Links to article:

weblife article gives a good list of materials with C:N ratios

compost fundamentals gives a description of the composting process

Not sure if I addressed your question as you expected, but I hope this helps.