MongoDB: Is it possible to search for two fields whose array sizes don't match?
Is this possible with the $size operator? ... so my Plan B will be to
  add two separate fields called numAccepted and numInvited ...


The $size operator matches any array with the number of elements specified by the argument. In this case you have to compare the size of two array fields within the same document. You cannot use MongoDB Query Language (MQL) operators for this purpose. 

The aggregation $size array operator returns the length of an array. To use aggregation operators within a find query, you have to use the $expr operator. Here is how it is done:

db.collection.find( { $expr: { $ne: [ { $size: "$customersInvited" }, { $size: "$customersAccepted" } ]  } } )


Note the $size and the $ne used in the above query are aggregation operators.