No, the table viewer is currently read only. The table viewer displays the current state of the data by generating a SQL query. The table viewer holds only 100 rows in memory at any given time, and the state of the viewer is completely independent of the underlying state of the table. If the table changes structure or values, the changes are not displayed until you refresh the viewer.
Unlike the data grid in SAS Enterprise Guide or the VIEWTABLE window in SAS Display Manager, the table viewer in SAS Studio is strictly a viewer. The ability to edit data in SAS Studio as well as offer data entry functionality similar to PROC FSVIEW and PROC FSEDIT is being considered for a future release.