Can you accept a LAHSO on your private pilot checkride?
First, let's see whether it's legal. FAA Order 7110.118 notes that:


  7. EXPLANATION OF CHANGES.
  
  The following changes apply to all LAHSO. 
  
  
  a. ...
  b. Solo student pilots will not conduct LAHSO. 
  


However, you could interpret that as not applicable to your situation, as you are not the sole occupant of the aircraft:


  14 CFR §61.87
  
  (a) General. ... The term "solo flight" as used in this subpart means that flight time during which a student pilot is the sole occupant of the aircraft...


Though it might be allowed, note it does not say must:


  AIM 4-3-11(b)
  
  
  ...
  Student pilots or pilots not familiar with LAHSO should not participate in the program.
  


I'd recommend against doing so because LAHSO can add to your workload, especially if you're a bit nervous on your checkride. Also, the AIM note on discouraging LAHSO is rather valid and if done improperly, can affect safety. Having said that, the examiner is likely to ask questions on LAHSO during your practical examination, especially since LAHSO is a special emphasis area in the PTS. This may include:


Requirements to accept a LAHSO clearance
ATC pharseology for LAHSO
Pilot responsibilities while carrying out LAHSO


In any case, always remember that you do not need to accept a LAHSO clearance -- if you do not feel comfortable with doing so, ATC will provide arrangements to land full-length on the same runway or another one. You should not accept a LAHSO clearance if you believe doing so would compromise safety.



Note: this does not necessarily apply to all situations where a student pilot is prohibited from doing something that a private pilot would be able to do.