Can a white (or other color) wire be remarked to serve as a grounding conductor?
To my understanding, no.


  250.119 Identification of Equipment Grounding Conductors. Unless required elsewhere in this Code, equipment grounding conductors
  shall be permitted to be bare, covered, or insulated. Individually
  covered or insulated equipment grounding conductors shall have a
  continuous outer finish that is either green or green with one or more
  yellow stripes except as permitted in this section. Conductors with
  insulation or individual covering that is green, green with one or
  more yellow stripes, or otherwise identified as permitted by this
  section shall not be used for ungrounded or grounded circuit
  conductors.


Note that 250.119 (A) and (B) do allow marking the wire green at the terminations for wires larger than 6 AWG.