Possible to use EntityStorageBase::loadByProperties() to specify that field is or is not empty?
Only in a narrow scope where "empty" for the field means the empty string ('') and it's stored as such in the DB.

EntityStorageBase::loadByProperties() uses a helper method, ::buildPropertyQuery(), that chains comparisons using the IN operator. As such, you can't use negation or special comparison cases (e.g. IS NULL if "empty" means NULL in the DB). 

Unless you have simple string comparisons for your field, you're better off skipping ::loadByProperties() and using EntityStorageBase::getQuery() to retrieve a query object that you can customize to fit a "empty" / "not empty" query.