Database of Multicellular and Unicellular organisms?
More like a comment:

It doesn't seem that such a database exists, but I think it's relatively easy to create a list of multicellular taxa and the rest should be considered unicellular. Since you use ncbi taxonomy, you can easily get higher-level parent for any species, so there is no need to define cellularity for individual species.

The challenging groups would be different algal and fungal taxa, but there are some good reference books. You also have to decide, whether to introduce a separate category for colonial/coenobial/filamentous organisms.