Not an easy way that works for all queries, no.
If the query is sorted by a unique field, you can use a DCount() expression
or a subquery to count the number of records. For example, if it is sorted
by the field ID from Table 1, you could do it by typing this expression into
the Field row:
MyCount: (SELECT Count(ID) FROM Table1 AS Dupe
WHERE Dupe.ID <= Table1.ID)
However, this subquery will need to be modified to match the WHERE clause in
your query, and won't work at all if the user right-clicks a field in the
query output, and sorts it differently.
Another alternative is to create a table with exactly the same fields as the
query, plus an AutoNumber field. Then change the field into an Append query
(Append on Query menu), and add the records to the table. The autonumber
then gives you the sequence.
If subqueries are a new concept, this might help:
http://allenbrowne.com/subquery-01.html