Yes,
it is possible to indirectly edit the columns of the
joined table and have the changes reflected through
the ArcMap join.
--Add the joined table to ArcMap and perform edits directly
on the table's data.
Changes will be reflected in the joined columns and
refreshed whenever ArcMap reads the table, such as
opening or activating the joined table. A benefit
to this approach is that schema changes made to the
joined table will also be reflected in the join.
--Edit the joined table in another software application.
Edits can be made to the joined table using Access
or other applications. Changes made to the joined
table in Access while it is open in ArcMap are cached
and it is necessary to refresh the table in ArcMap
to see the changes. If one of the joined fields is
being used as a Label Field, it is necessary to refresh
the map by clicking the Refresh Map button in the
lower left corner of the map display window to see
the updated labels.