That is VBA code to execute an SQL action statement. No Access query object is involved.
It doesn't work because variables must be concatenated. Reference to control on form is a variable. I prefer CurrentDb.Execute method:
CurrentDb.Execute "UPDATE wrkTable SET Chosen=True WHERE Department = '" & Forms!EdEnroll!Department & "'"
Forms!EdEnroll.Requery
If Department is a number field, remove the apostrophe delimiters.
Run Debug>Compile to catch VBA code syntax errors but it will not catch errors in SQL statements.