heap-only tuples, and constraints

Hi,

Question about heap-only tuples, and constraint checking.

Does this statement (UPDATE user SET email='newChangedVal',
password='existingVal') requires updating an index on user.password?
Or more generally, if an UPDATE includes an explicit but unchanged
value for an index column, does postgres need to also update the index
entries? Or does HOT apply only when indexed column is missing or not
explicit (i.e. password=password)?

Along the same line of thought as above, if password is a foreign key
column and if an UPDATE includes an explicit but unchanged value for
this fk column, does postgres need to check constraint satisfiability?

Thanks