Can an instrument procedure be intercepted from the middle and how?
Answer is yes.

FAA

ATC Section 6. Vectoring:


  When vectoring or approving an aircraft to deviate off of a procedure that includes published altitude restrictions, advise the pilot if you intend on clearing the aircraft to resume the procedure.
  
  PHRASEOLOGY−
  
  
    FLY HEADING (degrees), MAINTAIN (altitude), EXPECT TO RESUME (SID, STAR, etc.).
    
    
    
    DEVIATION (restrictions if necessary) APPROVED, MAINTAIN (altitude) EXPECT TO RESUME (SID, STAR, etc.) AT (NAVAID, fix, waypoint).
  
  
  NOTE− After a Climb Via or Descend Via clearance has been issued, a vector/deviation off of a SID/STAR cancels the altitude restrictions on the procedure. The aircraft’s Flight Management System (FMS) may be unable to process crossing altitude restrictions once the aircraft leaves the SID/STAR lateral path. Without an assigned altitude, the aircraft’s FMS may revert to leveling off at the altitude set by the pilot, which may be the SID/STAR’s published top or bottom altitude.
  
  
    (Position with respect to course/fix along route), RESUME OWN NAVIGATION, FLY HEADING (degrees).
    
    
    
    WHEN ABLE, PROCEED DIRECT (name of fix), RESUME (SID/STAR/transition/procedure).
  


ICAO

eurocontrol.int quotes ICAO Doc4444, 15th edition 2007:

12.4.1.4


  RESUME OWN NAVIGATION [DIRECT] (significant point) [MAGNETIC TRACK (three digits) DISTANCE (number) KILOMETRES (or MILES)].


12.3.2.1


  JOIN (specify) AT (significant point) AT (level) [AT (time)].
  
  Example: LGL123 join upper golf 1 at GORLU at FL330 at time three two.