I think that nitrogen deficit can only affect the plants much if the sawdust is mixed into the soil. If they are mixed together, the microbes eating the sawdust can steal N from the soil they are mixed with.
If the sawdust is only laid ON TOP OF the soil, as a top-dressed mulch, I think that the only place the N deficit can occur is in the top few millimeters of soil - the interface between N-starved sawdust and C-hungry soil. I don't think that microbes can reach out thousands of times farther than their own size to steal N from soil an inch away.
What would you say, Rick R? Is there any N deficit with top-dressing mulches, a little, a lot, or what? I assume we agree that sawdust mixed with soil causes more N deficit (like, a huge amount) than it does if layered on top.
I guess someone would have to do a study to be sure that fungi with long mycelia or hyphae can't digest cellulose at one end of the hyphae, and steal N with the other end, then transport energy compounds down and N up. My belief is that acti8ve internal transport like that is very "expensive" for a fungus to perform, so not very much of it happens.
But I've read many times that wood CHIPS cause N deficit only if mixed INTO soil (and seen it happen myself). A top-dressing of lots of wood CHIPS doesn't cause N deficit. Or so I've read in multiple places.
If a top-dressing of saw DUST were to decompose very fast (for example, if dusted with hydrated lime or maybe if dusted with some N source), organic compounds might leach downwards with rain. If enough of those leached into soil that was already N-starved, it might make enough difference to be detectable.
My general approach is to top-dress with wood CHIPS, not sawdust, so that air and rainwater can perk downwards unobstructed. Also, I can easily rake away a mulch of wood CHIPS when I need to. And few weeds will root in fast-draining wood CHIPS.
But any weed would love to root in sawdust, IF it can reach any N with its roots before it starves.
P.S. It might help avoid top-dress-N-deficit if you add any N fertilizer into the soil, and mix it in, BEFORE adding sawdust on top. If you add N on top of a top-dressing, the top-dressing is likely to catch and hold lots of the N, and accelerate the growth of anything breaking down the sawdust.
