If you file a flightplan with "NO SID", can you still get assigned a graphical ODP in your clearance?
ATC can indeed include an ODP in a clearance; this is from the ATC orders section 4-3-2:


  Where an obstacle departure procedure (ODP) has been published for a
  location and pilot compliance is necessary to ensure separation,
  include the procedure as part of the ATC clearance.  
  
  EXAMPLE−
  “Depart via the (airport name)(runway number) departure procedure.”
   Or
  “Depart via the (graphic ODP name) obstacle departure
  procedure.”


The "NO SID" note is exactly what it says, i.e. it applies to SIDs only. This is from the orders 4-3-3:


  If a pilot does not wish to accept an ATC clearance to fly a SID,
  he/she is expected to advise ATC or state “NO SID” in his/her flight
  plan remarks.


Note that SIDs and ODPs exist for slightly different reasons: SIDs are primarily to simplify communication and automation; ODPs are specifically designed to help ensure obstacle clearance and you can fly one without an ATC clearance (unless ATC assigned some other departure procedure). That means it's usually in your interest to fly an ODP if possible.

Having said all that, a pilot can always decline some or all of a clearance that he isn't capable of flying or is just uncomfortable with. But if you reject both SIDs and ODPs, then ATC has to vector you and that could easily cause delays, especially at a busy airport.