I can't tell you whether or not to use it but I can tell you
Some types of trees have fumes that can be toxic to animals. So if you cannot be certain what types of wood are in the sawdust... do not use. No cedar, no walnut and there are probably others to avoid.
Some folks say that chickens are more likely to eat dust size wood pieces as opposed to shavings and this can lead to impacted crops, etc.
It depends what they mean "sawdust". If it is really literally sawdust, it is too dusty for a coop, also it will tend to pack down into paper-mache that can be rather difficult to keep stirred and cleaned. If OTOH it is long curly shavings from a planer, or something like that, with little dust involved, then sure, go for it, especially if it is spruce/pine/fir. (Hardwood shavings are more apt to mold and thus need to be kept a closer eye on)
I buy sawdust for my hens, I believe it's pine, and I prefer it over "shavings". It's easier for me to clean the coop, as the clumps are dried and I can literally just rake them in a pile and dispose of. I then throw more sawdust down. I even use it in the run. I guess there could be different 'grades' of sawdust. The kind that I purchase it not extremley fine, however it is sawdust. I haven't had any problems.
If someone is offering you a bunch free- I say be most gracious and take it off there hands!
I use pine shavings, in my nest box's and the pen. It is in compressed bales. I pay $6.00 a bale and I can fit two bales in the trunk of my car. I find that the poo rakes out really easy. No problem with clean up. I agree that the sawdust will mat and like the name says, Saw-Dust! One of the things I like about the shavings is that it is dust free. I also deep litter, The chickens keep it stirred up.
We have used sawdust for the chicken house floor for years.
The fellow down the road has a small mill, we trade eggs for sawdust.
Sometimes he has shavings so we mix the two together.
It could either be a mix of fir, alder, birch, hemlock, maple or cedar wood.
Never had a problem.