Because of the enormous surface area of sawdust compared to coarse wood mulches, this provides a huge working area for microorganism to get busy breaking down the wood. But while they are working, they need nitrogen for the process, and they will suck up it up from the soil, using it for their purposes, and very little will be available for any plants. (So much so that you can hear the sucking noise... just kidding!
) When the sawdust is done composting, the locked up nitrogen will be released back into the soil. But how long that takes will depend on how much nitrogen is available at the start.
When I was child, in northern Minnesota we use to play around huge sawdust piles from my Granddad's sawmill. They were already decades old, always moist, yet never decayed. There wasn't any nitrogen available for the composting process. Nothing grew in those sawdust piles, not even weeds.
So using sawdust, even with added nitrogen fertilizer, will be a bumpy ride, because estimating how much nitrogen you need is a crap shoot. In the end, you'll be fine; but in between, I don't think so. Best to use the sawdust in a compost pile with ample green material as a nitrogen source.