Yes, it will. Even if there’s no match, the lookup has to occur to establish that there’s no match.
Worth measuring and based on how large. If you’re looking up on the _id field, it will still be quite fast.
To improve performance, you can use $facet or $unionWith; both with a $match operation for the fields.
If there’s a group operation, then facet works well. But there’s a 100MB per stage limit and the standard document limit of 16 MB for the final result . So if you want full/all documents, then you will need unionWith.
Do you have some example data?