Unfortunately I do not think cursors will work on joined tables. I think you would be better off using a dictionary with an update cursor. This code is untested but something like this should work:
import arcpy
# tables
source_tab = r"E:\Gampaha\51027202\CM51027202.gdb\CM51027202\PCL_Anno_New"
read_tab = r"C:\CMSupport.gdb\Conv_Tab"
# Create dictionary for update cursor
rows = arcpy.SearchCursor(read_tab)
cur_dict = dict((r.Nam_Idm, r.Name_Sin) for r in rows if r.Name_Sin)
del rows
# Update cursor to fill in rows
cur = arcpy.UpdateCursor(source_tab)
for row in cur:
if row.Text in cur_dict:
row.TextString = cur_dict[row.Text]
cur.updateRow(row)
del cur, row