Indeed she did. The violation of that oath can be construed as treason.
No, a mere failure to adhere to the Constitution is not in itself treason, as treason is well defined:
Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort. No Person shall be convicted of Treason unless on the Testimony of two Witnesses to the same overt Act, or on Confession in open Court.