If we run a N1QL query, that hits a cover index, but without order by, would it guarantee a deterministic order on query result, like, following the default order of the data saved in index?
Only way guarantee a deterministic order is ORDER BY. The OREDER BY follows leading index keys and when ever possible N1QL avoids sort
Adding an ORDER BY matching the index is effectively free. It does not add an actual sort. You can check this by adding the ORDER BY and using EXPLAIN on the query. If you put in an ORDER BY that does not match the index, then an OrderBy operator appears, containing a sort.