Short answer: Yes.

What kind of cedars are they? The local native "cedar" which is really Thuja ...

or are they Cedrus whatever...

I would be careful about the native cedar boughs (the Thuja) as mulch because nothing will grow under the cedars in my yard where there is a natural mulch of cedar boughs - not even sword ferns that are weeds everywhere else in my yard. I moved some to the area near the cedars and they struggled and died.

I think the cedars have some chemical that suppresses growth in other plants.

Cedar needles, of any genus, should be fine mulch.

Often the real problem growing stuff under the native cedars is the thick mat of roots the tree grows, and the fact that the native cedars can grow in soil that's too soggy for most other plants, and the heavy shade. Carrying the shed needles to mulch other areas of the garden should be fine.