What profile will a Boeing 737 NG follow after pushing the ALT INTV button?
What happens when pushing the ALT INTV button depends on the currently selected mode. You can find a full description from the FCOM in this answer.


VNAV Climb: The aircraft will remain in VNAV Climb mode and will follow the profile as programmed in the CLB page on the CDU.
Cruise: The aircraft will start an early descent:


  Early Descent
  
  To start an early descent, use DES NOW prompt on the DES page. An early descent can also be started by pushing the altitude intervention switch.
  
  
  
  (1) DES NOW (VNAV PTH)
  
  With a VNAV path descent planned, VNAV starts an early descent at 1000 fpm
  and captures the idle descent path. VNAV uses FMC SPD for the autothrottle
  mode and VNAV PTH for the pitch mode.
  
  (2) DES NOW (VNAV SPD)
  
  With a VNAV speed descent planned, VNAV starts an idle thrust early descent.
  VNAV does not attempt to capture the VNAV descent path. VNAV uses VNAV
  SPD for the pitch mode and the autothrottle commands IDLE, followed by ARM.


(Boeing 737 NG FCOM 11.31.36 - Flight Management, Navigation - Flight Management System Operation)

So in this case it depends on the VNAV descent that is planned in the FMC. If you have an altitude constraint selected, the aircraft will start a descent at 1000 feet per minute and intercept the idle descent path. Otherwise it will immediately start the speed descent as programmed in the DES page of the CDU.
VNAV Descent: The aircraft will remain in VNAV Descent mode, but the idle descent path can change due to the deletion of an altitude constraint. Should this result in the aircraft no longer being on the idle descent path, the mode will change from VNAV PATH to VNAV SPD and the aircraft follows the speed programmed in the DES page of the CDU. The same thing happens when all altitude constraints are removed.
Any other mode: Nothing happens. The ALT INTV button has no effect on other modes like V/S for example.