Unfortunately, no. Because a product can have infinite amount of tags and collections it would cause our product database to become unwieldy, and increase the time of product syncs dramatically. This issue is even more pronounced for shops with a large number of product variants. So for now, until we can tackle the technical challenge, you are left with Vendor and Product Type.
Hint: If you are not currently using the Vendor or Product Type field, start using it in a way that will let you more easily assign products using our bulk select and assignment function.