I would omit
the in both sentences.
My reasons are:
1. One would most often hear these sentences without
the.
2.
The is not needed to single out or specify -- the functions of
the -- which president or committee head.
3. A substantive (noun) objective complement is like a defining adjective: President Bush, Committee Head Jane.
4. The essential linking verb (which calls for an objective complement) is
to be. These sentences can be unambiguously reworded with a form of
to be and without
the:
Bush was President.
She was head of the committee. In contrast, the would be needed in: Bush was the second president to be impeached in twenty years. She was the oldest head of the committee. In these latter cases, the is needed to specify which president and which committee head.
5. I found these examples:
They elected Fressler chairman. ---Understanding Grammar, by Paul Roberts
The team elected the twins co-captains. ---dailygrammar.com
The group appointed the new member secretary. ---dailygrammar.com